Paul mentions several functions that the Jewish Law had in the story of salvation. One is that it informed Jews of exactly what God’s expectations were (7:7). At the same time, it demonstrated to those same well-intentioned Jews that they were unable to meet those expectations (7:14-15). The Law was like a child’s guardian, who taught Israel until it was old enough not to need the instructor anymore (Gal. 3:24). The coming of Christ points to that “maturity” in the story of salvation.
Paul even considered the Jewish Law to be the “power” of Sin (1 Cor. 15:56). Knowing the Law somehow seemed to aggravate the situation. The power of Sin over weak, human flesh seemed to thrive in the face of the Law (Rom. 7:13). The very fact of knowing God’s expectations seemed to make it even harder not to fail them.
When Paul speaks in such terms, he generally had in mind a part of the Jewish Law that later Christians would call the “moral law.” Here we refer to basic dos and don’ts like not killing or coveting or committing sexual immorality. What is confusing to us is that Paul also used the word Law to refer to other parts of the Jewish Law that later Christians would call the “ceremonial” law. This part of the Law included things like what Jews could not eat, touch, or wear. For Paul the Jew, the Law was of one piece, and so he used the same word for both parts of the Law. It is thus no wonder how much confusion and variation in interpretation we find out there!
So it is true that Paul did not believe a person could “earn” a right standing with God. He taught that all had sinned and that no one deserved God’s favor. But we would argue that this valid Protestant point was not really the focus of Paul’s own arguments. For Paul, the main issue he was facing was not faith versus works but Jew versus Gentile. Most of the time when Paul said that “works of Law” could not make anyone right with God (e.g., Rom. 3:28), he arguably was primarily picturing in his mind the parts that most separated Jew from Gentile—the “ceremonial” parts.
After all, it was the question of whether Jew and Gentile believer could eat together that sparked Paul’s teaching on this subject in Galatians. Romans 4 goes on to talk about Abraham’s circumcision as the main illustration in Romans. Paul’s basic point was that specifically Jewish practices like circumcision or food laws did not earn Jews any more of a right standing with God than the standing Gentiles started out having.
What is thus confusing about Paul’s argument is that he is saying two slightly different things when he said believers were not under the Law. In part he was arguing that Gentile believers did not have to worry about things like circumcision or food laws. But in part he was also saying that the power of Sin over us through the Law was done so that through the Spirit we might actually keep its basic moral expectations.