Did Paul really think his Jewish opponents saw themselves as being sinless?

Standard Protestant teaching says that the reason why works cannot justify us is "because we are sinners," which is another way of saying that if we were not sinners, then works could indeed save us. As I have noted elsewhere on this blog (e.g. here), Paul never suggests works could save even if we were sinless. In this post, I want to add another detail which goes against this Protestant idea, namely looking at whether the Jews ever considered themselves sinless. I will now turn to the Scriptures to show that the Jews clearly did consider themselves sinners, which thus totally undermines the Protestant Perspective on Paul.

As I was looking around for some Protestant quotes on this matter, I came across this gem from R.C. Sproul's ministry: 

God’s people were justified by faith alone under the Mosaic covenant even though some verses in the Law say the doing of its precepts brings righteousness and life. One of these is Leviticus 18:5, which Paul quotes in Galatians 3:12. We might conclude from a superficial reading of the Mosaic law that old covenant people were saved by works, not faith. Some Christians have held this position. However, the Torah shows us that while it reveals God’s righteous standard, our Creator knew that sinners could never save themselves by doing the Law. For example, the inclusion of sacrifices to atone for sin presupposes that the people will fail and have to look for another way to be justified.

The first sentence here says that under the Law people were justified by faith alone "even though" the Law says you are justified by works. How could the Bible say justification is by faith alone if it teaches justification by works? This claim is a blatant contradiction in thought, which is sadly so characteristic of the PPP. But that's not all! The quote also goes on to say that the Law included instructions on performing sacrifices to atone for sins, since it was obvious that nobody could be sinless. What Jew would go around considering themselves sinless when they were fully aware of the long chapters in Leviticus dedicated to instructions on atoning for sin? Why would God issue a Law that simultaneously demanded sinlessness and a means to atone for sin? Did a single Jew on the annual Day of Atonement, dedicated to atoning for all the sins of the Israelite nation, seriously think they were without sin?

A fellow Catholic recently pointed out to me this same truth is clearly found in the account of the Woman Caught in Adultery in John 8, where Jesus famously says: "Let he who is without sin cast the first stone." As we all know, one by one, the Pharisees and other bystanders walked away. This is because they all knew they were sinners. Indeed, it was no secret that throughout their own history, even the greatest of their members were sinners: "David did what was right in the eyes of the Lord and did not turn aside from anything that he commanded him all the days of his life, except in the matter of Uriah the Hittite." (1 Kings 15:5) How many Pharisees committed murder and adultery like David did? Few, if any. Yet how many of them would consider themselves more righteous than David? Again, few, if any. So why would the most elite Jews of Jesus' time consider themselves sinners while also thinking they could keep the law perfectly to be justified by their works? Clearly, the PPP thesis truly makes no sense and thus needs to be abandoned. 

Given these clear proofs, we can be sure that Paul was not addressing opponents who actually thought they could sinlessly keep the Law. This means that Paul had something else in mind when talking about the issue of sin within the context of justification (e.g. Romans chapters 1-3), which I'll address in a future post.