Some Reformed Protestants have commented to me that the Catholic Church doesn't have an official view of the Atonement and that the Catholic Church even permits the Reformed view of "Penal Substitution". The problem with these kinds of claims is that they don't understand what the Catholic Church means when the Church uses terms like "atonement" and "sacrifice" (and similar terms), so these Protestants end up reading foreign ideas into Catholic teaching. The fact of the matter is, the Catholic Church doesn't have to condemn every single error that comes up in history, especially if those errors are already condemned in other forms. So while you won't find any Church teaching that says "Penal Substitution is heresy," you will find the Church teaching things directly contrary to what Penal Substitution espouses. Typically, the Church lays out parameters for orthodoxy, and while one is free to work within those parameters, one is not free to transgress those parameters. For this post I'll be giving some examples of Catholic teaching that go against the concept of Penal Substitution, showing that a Catholic cannot embrace that view of the Cross and be within the parameters of orthodoxy and Catholic thought.
(1) The Catechism says: "The Church, following the apostles, teaches that Christ died for all men without exception" (CCC605). The reason why Calvinists (at least the consistent ones) believe in a doctrine called "Limited Atonement" (the idea that Jesus didn't die for all men but rather only for the elect) is because Penal Substitution logically necessitates it. If Jesus suffered the same punishment all people of history deserved, then everyone would be saved, and since we know for certain that everyone is not saved, then this logically leads one to conclude Jesus did not die for all. Given this, it is only possible to say that Jesus died for all men if "atonement" is understood in a different manner than that of Penal Substitution, and thus Catholics cannot embrace Penal Substitution. This raises a follow-up question: What does "atonement" mean for Catholics? I'll address that next.
(2) One Calvinist told me that Ludwig Ott's famous Catholic theology textbook, Fundamentals of Catholic Dogma, has a section on atonement that I should read because it will 'prove' that the Catholic view of atonement allows for the Protestant understanding. Here's what Fundamentals has to say on the matter of atonement:
By atonement in general is understood the satisfaction of a demand. In the narrower sense it is taken to mean the reparation of an insult: <Satisfaction is nothing more than compensation for an injury done to another.> (Cat. Rom. II 5, 59). This occurs through a voluntary performance which outweighs the injustice done. If such a performance through its intrinsic value completely counterbalances the grievousness of the guilt according to the demands of justice, the atonement is adequate or of full value . . . If the atonement is not performed by the offender himself, but by another in his stead it is vicarious atonement (satisfactio vicaria).
(Book3, Part 2, Section 10.1 & 10.3)
So "atonement" (also called "satisfaction") is doing a good work that counterbalances (or even over-balances) the injustice that was done. Ott draws this out from the Catechism of Trent's section on Penance, wherein a concise definition is given: "Satisfaction is nothing more than compensation for an injury done to another." And St Thomas himself teaches plainly in the Summa:
He properly atones for an offense who offers something which the offended one loves equally, or even more than he detested the offense. But by suffering out of love and obedience, Christ gave more to God than was required to compensate for the offense of the whole human race. (ST 3:48:2)
This is a good foundation to lay, because this is the essence of the concept of Atonement (Satisfaction) that the Church endorses and what Scripture itself teaches.  There is nothing wishy-washy about this concept; it's a firmly established idea within Catholic tradition. There are no alternate definitions out there. And just as Thomas explains Jesus making atonement by means of suffering out of love and obedience, so too the Catechism explains it: "It is love to the end that confers on Christ's sacrifice its value as redemption and reparation, as atonement and satisfaction" (CCC#616). And the Compendium says on paragraph 122: "Jesus freely offered his life as an expiatory sacrifice, that is, he made reparation for our sins with the full obedience of his love unto death."  Notice that it's not receiving our punishment in which atonement is made, but rather the good work of Christ's commitment to loving sinful man even in the midst of persecution, hence why Christ's sacrifice is called a "pleasing aroma" in Ephesians 5:2 (as opposed to the stench of guilt which arouses God's wrath).
On the other hand, the Protestant view of "atonement" is that in which the guilt and punishment due to one person is transferred over to another. This Protestant understanding of atonement is foreign to Catholic tradition and the Bible. (More on this later.) In the true meaning of atonement, nothing logically demands nor requires guilt and punishment to be transferred. This also explains why the Catholic side speaks of Christ offering up a sacrifice while the Protestant side speaks of (God's) wrath being poured down on the sacrifice. 
(3) If good deeds are what cause atonement, then why is there so much talk of Jesus suffering? This question is especially relevant given that Jesus did in fact shed blood and die, and we know death is clearly a punishment of some kind. Since the mention of suffering suggests undergoing a penalty or punishment, this would thus seem to suggest Jesus was punished in our place, and thus supporting the Protestant claim. This is perfectly understandable, and this line of reasoning is why Penal Substitution is so easily affirmed. But this conclusion is very wrong for a couple of reasons.
Before addressing the problems, we must define what death is. Death does not mean you cease to exist, but rather death means that you now exist under a different condition: You begin your existence in life as a person existing with a compound nature of body and soul perfectly united, but upon death your soul has separated from your body. You as a person continue to exist within your soul alone, while your body suffers decay and awaits the ultimate "healing" (reuniting body and soul as they were never intended to be separated) coming from the Resurrection at the end of time.
What was just described is often called "physical death," even though it's properly and simply called death. But there is also a metaphorical death called "spiritual death" which occurs when you break communion with God. When you sin gravely, you lose sanctifying grace and thus the Trinity no longer indwells within your soul, hence the term "mortal sin" (sin which brings death [of the person's soul]). This is death in a supernatural way (since grace is not natural to man), and so death of this form is infinitely worse than natural death.
When Adam sinned, he underwent both types of death, and so do we. From this, Protestants understandably argue that Jesus must have undergone both types of death as well if He was truly going to suffer the punishment we deserve. Protestants say that for Penal Substitutionary Atonement to work, Jesus must have endured the spiritual death we deserved, the break off communion with God, otherwise Jesus wouldn't be suffering the punishment our guilt deserves. But this claim is incompatible with Catholic dogma for two reasons.
First of all, Catholicism teaches what the Scriptures plainly teach, that Jesus only endured a physical death, without any mention of spiritual death. For example, in paragraph 624 the Catechism says:
"In his plan of salvation, God ordained that his Son should not only "die for our sins" but should also "taste death," experience the condition of death, the separation of his soul from his body, between the time he expired on the cross and the time he was raised from the dead."
This quote is clearly talking about physical death only, which began the moment He died on the Cross (not before) and lasted until the Resurrection. And the Catechism of Trent confirms this in the Lesson on Article IV of the Apostles Creed (where the Creed says Christ was "crucified, died, and buried"):
The pastor should explain that these words present for our belief that Jesus Christ, after He was crucified, really died and was buried. It is not without just reason that this is proposed to the faithful as a separate object of belief, since there were some who denied His death upon the cross. The Apostles, therefore, were justly of opinion that to such an error should be opposed the doctrine of faith contained in this Article, the truth of which is placed beyond the possibility of doubt by the united testimony of all the Evangelists, who record that Jesus yielded up the ghost. . . . When, therefore, we say that Jesus died, we mean that His soul was disunited from His body.
Notice that spiritual death, which is more important in the Protestant scheme, is strikingly absent! Again, it is plain that when the Church speaks of Christ suffering death, the only thing meant is a physical death, not a spiritual death.  By this fact alone, the Church dogma doesn't allow Penal Substitution, since He didn't suffer the right type of punishment the Protestant view requires (i.e. spiritual death by the breaking of communion with the Father).  But there's more!
Second of all, it's theologically impossible for Christ to undergo spiritual death. Basic Christology, which was confirmed in the Ecumenical Councils, is reiterated plainly throughout Catholic tradition, and particularly clear many places in the Catechism, with paragraph 650 being the most helpful:
The Fathers contemplate the Resurrection from the perspective of the divine person of Christ who remained united to his soul and body, even when these were separated from each other by death: [Gregory of Nyssa says] "By the unity of the divine nature, which remains present in each of the two components of man, these are reunited. For as death is produced by the separation of the human components, so Resurrection is achieved by the union of the two."
Again, this is basic Christology, and Catholics have always been careful to not violate Christology in any sense.  Unfortunately, Protestants often eschew advanced theology and philosophy, so they run right into Christological heresy when they insist that Jesus underwent a spiritual death. This weak theological foundation is why you have big name Reformed Protestants saying Jesus was cut-off from the Father, that the Father broke fellowship with the Son, that the Son was "damned," etc. But this is plainly impossible once you realize Jesus is a Divine Person with a Divine Nature and human nature permanently united. How could Jesus spiritually die (the soul losing the indwelling of the Holy Trinity) when the union was so permanent that His Divinity remained united to his body and soul even after the two separated? And even more problematic is that "spiritual death" means it was the Divine Person of Son who would be cut-off from the Divine Person of Father, not merely the Son being cut off from human nature. In other words, it's heresy (Nestorianism) to suggest the Divine Son (a Person) could only suffer broken communion in His humanity, since it is Persons who form communion with other Persons, not natures (alone) in communion with natures. So "cutting off" the Son would, by definition, destroy the Trinity, since it severs Christ's very Sonship.
Even though Protestants are insistent that the Trinity was not destroyed, they lack the theological foundation to realize that is in fact what Penal Substitution amounts to. And since the Catholic Church affirms basic Christology, clearly affirmed in the above quotes regarding Christ's death (the very thing under consideration now), this makes it impossible for any Catholic to affirm Penal Substitution.
(4) How is physical suffering and death for a mere few hours sufficient to atone for an infinite offense against God? Catholic theology has a good explanation for this, and it's been consistently taught by all the great minds of the Church, especially by Aquinas (ST 3:48:2.3): "The dignity of Christ's flesh is not to be estimated solely from the nature of flesh, but also from the Person assuming it--namely, inasmuch as it was God's flesh, the result of which was that it was of infinite worth." And in Ott's Fundamentals we read:
The intrinsic reason of the adequacy of Christ's atonement lies in the Hypostatic Union. Christ's actions possess an intrinsic infinite value, because the [person doing the action acting] is the Divine Person of the Logos. Thus Christ's atonement was, through its intrinsic value, sufficient to counterbalance the infinite insult offered to God.
As a crude analogy, think about the King in a game of Chess. The King's life is of infinite worth, worth more than even all the other pieces put together. So a loss of just the King is a loss of infinite value. In fact, even the smallest suffering Christ underwent was sufficient to provide not just an atonement of equal value to the offense of all man's sins, but in fact Christ's smallest deeds sufficed as a super-abundant atonement. And this is well established Catholic teaching, as Ott references Pope Clement's VI Papal Bull Unigenitus Dei Filius in 1343, in which Clement taught that Jesus,
"Who innocent, immolated on the altar of the Cross is known to have poured out not a little drop of blood, which however on account of union with the Word would have been sufficient for the redemption of the whole human race, but copiously as a kind of flowing stream" (Denzinger #550).
Though this quote can be awkward to read, in it the Catholic Church teaches that a mere single drop of Christ's blood would have been sufficient for the redemption of the world. But in God's great wisdom, it wasn't just a little drop of blood was shed, but rather rivers of blood, to more magnificently show forth God's love. In fact, the very Catholic language and teaching that Jesus make "super-abundant" (not merely equivalent) satisfaction for our sin is illogical in Penal Substitution, because then it would mean Jesus suffered a punishment far worse than what our sins deserved to be punished for.
Since a Protestant cannot logically affirm (nor have I seen in practice) a mere drop of Christ's blood would have been sufficient (even super-abundant), this shows that the Catholic understanding of the Atonement is incompatible with Penal Substitution.
(5) But even if we say Jesus suffered only physical death, isn't that still saying Jesus endured a punishment? It is only true in the broad, non-judicial sense of "punishment" can we say that Jesus was punished for us. In fact, as an earlier footnote makes clear, Gospel accounts never mention the Father as inflicting harm on Christ. The only source of Christ's pains came from the miserable physical persecutions done by men, which Christ calmly endured as the "lamb who remained silent," and in this peaceful enduring of suffering turned this around into a sacrifice. As Ott explains:
The act of sacrifice consisted in the fact that Christ, in a disposition of the most perfect self-surrender, voluntarily gave up His life to God by permitting His enemies to kill Him, although He had the power of preventing it.
(Fundamentals of Catholic Dogma, Bk3:Pt2:Ch2:Sec8)
And St Thomas confirms:
"Christ's Passion was indeed a malefice on His slayers' part; but on His own it was the sacrifice of one suffering out of charity. Hence it is Christ who is said to have offered this sacrifice, and not the executioners" (ST 3:48:3.3)
So Christ, acting as High Priest, offered up his life by refusing to hate his enemies in the midst of persecution.  This is precisely what St Peter meant when he interpreted Isaiah 53 for us in his First Epistle (I wrote about this HERE). I don't really see how Protestants can affirm Christ as High Priest because in the Penal Substitution view it is God inflicting the "punishment" on the sacrifice, which effectively strips the High Priesthood from Jesus and gives it to the one Person who cannot be High Priest, God the Father (Who is on the receiving end of the Sacrifice)! (I wrote about this in ANOTHER ARTICLE). So, yet another reason why the Catholic understanding of Atonement isn't compatible with Penal Substitution.
(6) Why do Catholic documents state that Jesus endured the worst sufferings humanly possible, particularly in His soul, if not to indicate He suffered the (equivalent) pains of hellfire itself? This is a good question and requires some explanation, as well as sufficiently understanding all of what has been said up to this point in the article.
The Catechism of Trent explains in Article IV of the Creed (quoted freely):
It cannot be a matter of doubt that His soul as to its inferior part was sensible of these torments; for as He really assumed human nature it is a necessary consequence that He really, and in His soul, experienced a most acute sense of pain. Hence these words of the Savior: My soul is sorrowful even unto death. ... Although human nature was united to the Divine Person, He felt the bitterness of His Passion as acutely as if no such union had existed.
That Christ our Lord suffered the most excruciating torments of mind and body is certain. In the first place, there was no part of His body that did not experience the most agonizing torture. His hands and feet were fastened with nails to the cross; His head was pierced with thorns and smitten with a reed; His face was befouled with spittle and buffeted with blows; His whole body was covered with stripes.
His agony was increased by the very constitution and frame of His body. Formed by the power of the Holy Ghost, it was more perfect and better organized than the bodies of other men can be, and was therefore endowed with a superior susceptibility and a keener sense of all the torments which it endured. . . . Christ our Lord tempered with no admixture of sweetness the bitter chalice of His Passion but permitted His human nature to feel as acutely every species of torment as if He were only man, and not also God.
It is important to distinguish between Christ suffering divine spiritual torments (i.e. the Father's wrath, spiritual death) versus suffering human emotional torments. This is why the Catechism speaks of Christ suffering in the "inferior part" of His soul, meaning the emotions and mental anguish. Aquinas elaborates on what this mental anguish consisted of in ST 3:46:5,
For Christ suffered from friends abandoning Him; in His reputation, from the blasphemies hurled at Him; in His honor and glory, from the mockeries and the insults heaped upon Him; in things, for He was despoiled of His garments; in His soul, from sadness, weariness, and fear; in His body, from wounds and scourgings.
Note that none of this suffering of Christ's soul is said to be of the divine type, God's anger, etc, as Protestants teach. In that link, Aquinas specifically rules out the idea Jesus suffered every type of suffering, because Jesus didn't endure every type of suffering, most especially not being cut-off from the Father. And that's the key. Even though Jesus was made capable of suffering worse than anyone ever suffered, this wasn't due to suffering certain types of pains. And thus there's no actual basis to say that Jesus suffered the equivalent of hellfire or anything similar, because intensity of suffering isn't the same as type of suffering. Christ's sufferings of body and soul were of the 'temporal' ('physical') type only.
Such distinctions show that in Catholic teaching, Jesus did not (and earlier it was shown He could not) suffer the pains of being spiritually cut-off from the Father, as Penal Substitution requires, despite affirming that Jesus did in fact endure the worst suffering a person has ever suffered, including in His soul.
(7) A Reformed Protestant presented a few quotes (which I'll share below) from John Paul II commenting on Jesus' words "My God, why have you forsaken me" that seem to be compatible with the Protestants understanding of those words. What did John Paul II mean in those quotes?
First off, I've covered this verse numerous times, so please just search my blog if you want to know more. Briefly, the Reformed interpretation is that Jesus was spiritually cut-off from the Father when He uttered these words, as the Father's wrath poured down upon Him while on the Cross. The Reformed insist that if you fail to affirm their interpretation of Jesus' words, then you've missed the very heart of Jesus' suffering on the Cross. But Catholic tradition is clear how these words are to be understood, with St Thomas Aquinas in his survey of ancient Christian commentary giving us the understood meaning: "God is said to have forsaken Him in death because He exposed Him to the power of His persecutors; He withdrew His protection, but did not break the union."  No Catholic document I've ever seen permits reading Christ's words as signifying Jesus enduring spiritual cutting-off, broken fellowship, the Father's wrath, etc. In fact, such talk is the furthest thing from the orthodox Catholic mind, as I've shown throughout this article thus far.
Now the two quotes from Blessed John Paul II are as follows, which I'll comment upon as I present them:
More than an experience of physical pain, his Passion is an agonizing suffering of the soul. Theological tradition has not failed to ask how Jesus could possibly experience at one and the same time his profound unity with the Father, by its very nature a source of joy and happiness, and an agony that goes all the way to his final cry of abandonment. The simultaneous presence of these two seemingly irreconcilable aspects is rooted in the fathomless depths of the hypostatic union.
(Apostolic Letter: Beginning the New Millennium, paragraph 26)
From this quote, the Protestant made the claim that John Paul is saying here that Jesus could, in some mysterious manner, experience both perfect communion with the Father while simultaneously experience cutting-off from the Father. It would seem two polar-opposite ideas are being affirmed, and thus the Reformed are free to say Jesus was simultaneously suffering eternal damnation while at the same time enjoying perfect Heavenly bliss.
With all that I've said thus far, it shouldn't be hard to see the fallacy and error in this Protestant's claim. First of all, this Protestant is assuming John Paul is actually talking about Jesus being spiritually cut-off from the Father. But that's not correct (which I'll further demonstrate in a bit). Second of all, John Paul is clear that the great theological minds have asked and addressed this question, meaning it is not an open question that Catholics can just believe as they please on. The great theological minds have demonstrated what is true and what is false on many facets of the Mystery of Salvation. As I've already shown, there's no basis whatsoever to think the great Catholic minds ever saw Jesus suffering God's wrath as an option. Thirdly, it's absurd to think that John Paul (or any great Catholic theologian) was asserting a blatant contradiction, as if Jesus could be simultaneously in communion and not-in-communion with the Father. That's ridiculous.
Now for John Paul's explanation in his very next paragraph:
Faced with this mystery, we are greatly helped not only by theological investigation but also by that great heritage which is the "lived theology" of the saints. The saints offer us precious insights which enable us to understand more easily the intuition of faith, thanks to the special enlightenment which some of them have received from the Holy Spirit... Not infrequently the saints have undergone something akin to Jesus' experience on the Cross in the paradoxical blending of bliss and pain. In the Dialogue of Divine Providence, God the Father shows Catherine of Siena how joy and suffering can be present together in holy souls: "Thus the soul is blissful and afflicted: afflicted on account of the sins of its neighbor, blissful on account of the union and the affection of charity which it has inwardly received. These souls imitate the spotless Lamb, my Only-begotten Son, who on the Cross was both blissful and afflicted".13 In the same way, Thérèse of Lisieux lived her agony in communion with the agony of Jesus, "experiencing" in herself the very paradox of Jesus's own bliss and anguish: "In the Garden of Olives our Lord was blessed with all the joys of the Trinity, yet his dying was no less harsh. It is a mystery, but I assure you that, on the basis of what I myself am feeling, I can understand something of it".14 What an illuminating testimony!
So what John Paul was talking about is simply this: How can a person who is so closely in communion with God also suffer 'negative' feelings like sadness, affliction, loneliness, etc? Well, since it's not a contradictory proposal, it's not impossible. But it certainly is mysterious, because you'd think that being in such intimate communion with God would include a certain comfort and safety that precludes feelings of sadness and such. Clearly, John Paul was not suggesting Jesus was enduring spiritual torments by God's angry wrath upon Him! Instead, Jesus' 'cry of final abandonment' is to be understood more along the lines of (but infinitely more acute than) the sadness that we all feel when in the midst of major suffering we ask ourselves "Why is God letting this happen to me?"
The second quote this Protestant provided was from John Paul's General Audience lecture from November 30, 1998, where the topic of that day was Christ's words of abandonment.
Here one can sketch a summary of Jesus’ psychological situation in relationship to God. The external events seemed to manifest the absence of the Father who permitted the crucifixion of his Son, though having at his disposal “legions of angels” (cf. Mt 26:53), without intervening to prevent his condemnation to death and execution. In Gethsemane Simon Peter had drawn a sword in Jesus’ defense, but was immediately blocked by Jesus himself (cf. Jn 18:10 f.). In the praetorium Pilate had repeatedly tried wily maneuvers to save him (cf. Jn 18:31, 38 f.; 19:4-6, 12-15); but the Father was silent. That silence of God weighed on the dying Jesus as the heaviest pain of all, so much so that his enemies interpreted that silence as a sign of his reprobation: He trusted in God; let God deliver him now, if he desires him; for he said, ‘I am the Son of God’ (Mt 27:43).
In the sphere of feelings and affection this sense of the absence and abandonment by God was the most acute pain for the soul of Jesus who drew his strength and joy from union with the Father. This pain rendered all the other sufferings more intense. That lack of interior consolation was Jesus’ greatest agony.
However, Jesus knew that by this ultimate phase of his sacrifice, reaching the intimate core of his being, he completed the work of reparation which was the purpose of his sacrifice for the expiation of sins. If sin is separation from God, Jesus had to experience in the crisis of his union with the Father a suffering proportionate to that separation.
Everything seems to be perfectly easy to understand and right in accord with the traditional Catholic interpretation of that verse. But then John Paul seems to throw a curve ball at the last sentence. This Protestant claims that in this last sentence, John Paul is indeed saying that Jesus did in fact suffer the equivalent pains of a lost soul in hellfire suffers. My response simply is that this is reading too much into the text. The context gives no reason to think this abandonment is that of a cut-off soul, and in fact the context already shows the type of abandonment. Jesus did experience the worst sufferings imaginable, and if the Father permitted all this to happen, then yes it's a profound mystery a loving God would allow that to happen to anyone, particularly His Son. And the fact that Jesus was still alive when He said "Father, into your hands I commend my Spirit" is in no way compatible with the idea that the Father was spiritually cut-off from Jesus.
In the end, these quotes this Protestant provided are simply pure desperation, scraping for whatever scraps Protestants can get their hands on to salvage a horribly blasphemous and unbiblical teaching.
Hopefully you enjoyed all this, and sorry for making it so long. I originally intended it to be much shorter.
 Ott's Fundamentals goes onto say: "When Holy Scripture designates Christ's precious blood, or the giving up of His life, as a ransom-price for our sins, the basic thought is that the atonement offered is of equal value to the guilt of the sins. 1 Peter 1:19; 1 Cor 6:20; 1 Tim 2:6"
And the Catechism of Trent (Lesson on Article IV of the Apostles Creed) says: "The price which He paid for our ransom was not only adequate and equal to our debts, but far exceeded them."
 Ott's Fundamentals also explain what "sacrifice" means:
By sacrifice is understood in the widest sense, the surrender of some good for the sake of a good aim. The religious meaning attaching to sacrifice in the wider sense is every inner act of self-surrender to God, and every outer manifestation of the inner sacrificial disposition, e.g., prayer, alms-giving, mortification. Cf. Ps 51:19; 141;2; Hos 14:2; Ecclus. 35:4; Rom 12:1 In the narrower liturgical sense one takes sacrifice to mean an external religious act, in which a gift perceptible to the senses is offered by an ordained servant of God in recognition of the absolute sovereignty and majesty of God, and, since the Fall, in atonement to God.
Nothing in this definition of "sacrifice" has anything to do with punishing the sacrifice in place of another. No transfer of punishment is taking place. See also Aquinas in ST 3:48:3 where "sacrifice" is similarly defined, and here I briefly quote: "A true sacrifice is every good work done in order that we may cling to God in holy fellowship."
 With that in mind, even though the end of the Fundamentals quote I gave says the Catholic view can be called called "Vicarious Atonement" (substitutionary atonement) it is crucial to keep in mind that "atonement" is being defined in a radically different sense than the Protestant Penal Substitutionary Atonement view. This is one reason why the Catholic Church doesn't simply condemn "Penal Substitution" by name, because terms alone aren't everything, concepts and definitions are what matter. And from this you can also see that the Protestant isn't even using the term "atonement" in a valid sense.
 John Calvin even admits the Creed is speaking only of physical death for Christ, but in a desperate attempt to find proof that Jesus died spiritually, Calvin went to the next clause in the Creed, which speaks of Jesus "descending into hell." In Calvin's Institutes 2:16:10, Calvin says, briefly:
But after explaining what Christ endured in the sight of man, the Creed appropriately adds the invisible and incomprehensible judgment which he endured before God, to teach us that not only was the body of Christ given up as the price of redemption, but that there was a greater and more excellent price - that he bore in his soul the tortures of condemned and ruined man.
On the surface, this clause can be mistaken to mean Jesus suffered hellfire and spiritual death. But Catholic tradition has always been clear that Jesus didn't endure hellfire, and rather this clause is talking about Jesus "descending into Hades" to rescue the Old Testament Saints on Holy Saturday, which is also why the Creed puts this clause after mentioning Christ's death and burial (signifying it's not part of His suffering). The Catechism of Trent speaks directly on this clause, explicitly saying that this was not the hell of the damned where Jesus went, but rather that "To liberate these holy souls, who, in the bosom of Abraham were expecting the Saviour, Christ the Lord descended into hell," and "Christ the Lord descended, on the contrary, not to suffer, but to liberate the holy and the just from their painful captivity." The Catechism says on this point that "he descended there as Savior" (See also CCC 632-633; Compendium Sec 125). So this "descent" of Christ had nothing to do with divine punishments.
 The Gospel accounts are clear that it was wicked men who inflicted the harm on Jesus, with no mention of the Father pouring out his wrath on the Son. I wrote about this HERE in an important article.
 And in CCC630: "During Christ's period in the tomb, his divine person continued to assume both his soul and his body, although they were separated from each other by death."
The Catechism of Trent confirms this, saying: "When, therefore, we say that Jesus died, we mean that His soul was disunited from His body. We do not admit, however, that the Divinity was separated from His body. On the contrary, we firmly believe and profess that when His soul was dissociated from His body, His Divinity continued always united both to His body in the sepulchre and to His soul in limbo."
 The Catechism of Trent speaks of this matter as well in Article IV of the Creed - all quotes trimmed down for size and without the use of ellipses:
This kind of death was chosen by the Saviour because it appeared better adapted and more appropriate to the redemption of the human race; for there certainly could be none more ignominious and humiliating. Not only among the Gentiles was the punishment of the cross held accursed and full of shame and infamy, but even in the Law of Moses the man is called accursed that hangeth on a tree. [Gal 3:13]
He therefore offered Himself not involuntarily or by compulsion but of His own free will. Going to meet His enemies He said: I am he; and all the punishments which injustice and cruelty inflicted on Him He endured voluntarily. Besides, to increase the dignity of this mystery, Christ not only suffered for sinners, but even for those who were the very authors and ministers of all the torments He endured.
Gentiles and Jews were the advisers, the authors, the ministers of His Passion: Judas betrayed Him, Peter denied Him, all the rest deserted Him. It was the punishment usually reserved for the most guilty and atrocious malefactors, a death whose slowness aggravated the exquisite pain and torture.
Christ's pains (the "punishment" of the Crucifixion) came strictly from wicked men, no mention of Jesus enduring the Father's wrath. And it was these punishments that Christ endured voluntarily, to use this patient endurance of hardship as His very sacrifice.
 In the Summa, St Thomas again explains what "forsaken" refers to: "by not shielding Him from the Passion, but abandoning Him to His persecutors" (ST 3:47:3).