To supplement the last post I made, a commonly abused text that I regularly see Protestants quote when attempting to prove Penal Substitution from Scripture is Hebrews 9:22, "without the shedding of blood there is no forgiveness of sins." They interpret this to mean that God cannot forgive unless someone pays the ultimate price for sin, taking your guilt and dies in your place.
On the surface level, this reading does make sense, but ripped out of context and completely misunderstanding the Levitical Sacrificial system (which I've written about elsewhere), that reading falls immediately flat. In this post I will focus simply on the context and show just how off the mark this Protestant claim is.
The context here is some of the richest in the Bible, being a place where the old and new testaments (covenants) are compared side-by-side. As you read the following passage, keep in mind that I've replaced the terms used in the ESV with the term "testament" because thats the Greek term (diatheke) used from verse 15 to 20. For whatever reason, many translations are very inconsistent in how they translate "testament" here, mixing in terms like "Will" and "Covenant," which I see as very bad form because Paul was using the same term throughout and clearly wanted people to connect the dots.
15 Therefore [Jesus] is the mediator of a new [testament], so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first [testament]. 16 For where a [testament] is involved, the death of the one who made it must be established. 17 For a [testament] takes effect only at death, since it is not in force as long as the one who made it [Greek: testator] is alive. 18 Therefore not even the first [testament] was inaugurated without blood. 19 For when every commandment of the law had been declared by Moses to all the people, he took the blood of calves and goats, with water and scarlet wool and hyssop, and sprinkled both the book itself and all the people, 20 saying, “This is the blood of the [testament] that God commanded for you.” 21 And in the same way he sprinkled with the blood both the tent and all the vessels used in worship. 22 Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins. 23 Thus it was necessary for the copies of the heavenly things to be purified with these rites, but the heavenly things themselves with better sacrifices than these.
The first thing to notice is that Protestants only quote the second half of 9:22 and ignore the first half, since they don't see how it fits. But what Paul is saying here is that forgiveness of sins is connected to the purifying by blood. The link between blood purifying and sins being forgiven is well established in the Bible (e.g. Heb 9:13-14; 10:29; 1 Jn 1:7; Rev 1:5). This is why Catholics say justification is based upon (or includes) sanctification, rather than something that merely accompanies justification (as Protestants teach).
The second and more important thing to notice is that the "death" and "blood" mentioned here is not about transferring a punishment, but rather inaugurating a covenant (also called testament). Thus, the language Paul is using here is that of something along the lines of a "Last Will and Testament", distinguishing between the Old Testament and the New Testament dispensations.
This is interesting because it sheds a new light on how Christ's death is understood. The analogy given in verses 16-17 is that of a Last Will that a parent writes of how he wants the inheritance to be split up and which goes into effect upon their death, inaugurating a new dispensation of sorts. Clearly this death of a parent doesn't have anything of the nature of Penal Substitution about it, so this strongly suggests that Penal Substitution is not the model which Christ's death patterned after in ushering in the new testament.
To build immediately on that, verses 18 and following say the old testament was inaugurated in this death/blood fashion, and yet Moses wasn't resorting to Penal Substitution when he inaugurated the old testament (Exodus 24:1-11). Thus, the death/blood of Jesus in patterning after that when instituting the new testament likely wouldn't have had the nature of Penal Substitution either.
The way I see this, the death inaugurates a new dispensation, which makes sense in a way (e.g. the Resurrection signifies a new way of living and new hope). The sprinkled blood then serves the purpose of consecrating the members for their new life under the covenant (Heb 9:13-14). This death is 'natural' in the sense that, after Adam, suffering became a 'natural' part of life, but it carries with it a bitterness and 'sting' since we all know suffering and death is not enjoyable. In becoming man, Jesus both made Himself subject to natural suffering and natural death (mortality), and in getting circumcised put Himself under the Mosaic Testament and made Himself subject to suffering and death at the hands of the Jews. This suffering in virtue of the Incarnation addressed in a 'medicinal' way (e.g. destroying death) the global sin-death problem, while the suffering under the Mosaic Testament addressed the violated covenant problem the Jews found themselves in (Heb 9:15) that was in a sense stalling God's promise to Abraham from being fulfilled in reaching the Gentiles (Gal 3:13-14). There's probably more that could be explored here, so I definitely have some pondering to do.