It is a big statement to make, but I believe that the vast majority of Christian interpreters of Paul’s teaching in Galatians and Romans have failed to understand Paul’s argument in the historical context of his day. The major theological issue for the early church (as the calling of the Council of Jerusalem proves) was the Judaizing issue. The issue was basically: Can Gentiles be saved as Gentiles, or do they have to come under the framework of the Mosaic covenant to be justified?
The key to understanding Paul’s argument in Galatians and Romans lies in realizing that his argument is a salvation-historical argument. That is, Paul was attempting to answer the question: How are people saved now that the new covenant in Christ has come? Reflecting the covenantal particularism of the orthodox Judaism of the day, the Christian Judaizers believed that, even though the new covenant had come in Jesus Christ, the new covenant fit neatly into the framework of the Mosaic covenant, leaving the law of Moses fully intact, and thereby restricting faith participation to those who were members of Israel. This is why they put pressure on Gentile Christians to be circumcised (if male) and to follow the law of Moses (Acts 15:1, 5). Paul’s argument is that the new covenant in Christ is actually co-extensive with the still yet earlier Abrahamic covenant, under which a gentilic faith response to God was possible (as proved by the faith of uncircumcised, gentilic Abraham himself).
In Galatians and Romans, Paul was concerned to contrast the requirement of faith under old covenant with the requirement of faith under the new covenant. The term law was Pauline and Jewish code for the Mosaic covenant, and the expression the works of the law was the standard Jewish way of referring to the covenant faithfulness that God required of Israel under the terms of the Mosaic covenant as per Ps 119:30, where the writer speaks of faith in terms of setting his heart on torah. Paul was primarily contrasting the old way of covenant faithfulness under the Mosaic covenant (which was required as the proper response under the old covenant, but had recently been superseded with the coming of Christ) with new (Abrahamic-type) way of covenant faithfulness to Jesus as revealed in the gospel, which Gentiles could participate in.
Paul sought to prove that the new covenant is more Abrahamic in nature than Mosaic. His main proof at this point was the evidence of word association in the Scriptures that linked the new covenant with the Abrahamic covenant. Employing a common rabbinic method of exegesis, Paul noted (as we see in Rom 1:16–17; 4:3, 9, 22; Gal 3:6, 11) that the word והאמן and he believed is used of Abraham in Gen 15:6, and the related word אמונה faith is used of the new covenant in Hab 2:4 (which is part of an eschatological prophecy). That common terminology allows us to link the Abrahamic and new covenants together, the implication being that, if Abraham could believe in God and be justified as a Gentile (i.e., before he was circumcised), then the same thing applies under the new covenant: Gentiles can be justified under the new covenant apart from submission to the law of Moses. Paul also argued that the Sinaitic covenant was just a temporary, intervening covenant (a kind of narrowing down of the Abrahamic covenant for the purpose of regulating the singular nation of Israel until the coming of Christ). Therefore, with the coming of Christ, the old covenant has been subsumed by the new covenant, thus allowing Gentiles to participate in salvation through faith in the Messiah. The new covenant is not just a continuation of the old covenant. The new covenant actually eclipses and supersedes the old, allowing righteousness to be opened up to the nations, in fulfillment of God’s promise to Abraham (Gen 12:3).
Paul’s argument in Galatians and Romans is a salvation-historical argument that deals specifically with the major historical issue for the church in his day: the Judaizing problem. It is not a general argument about believing versus doing (as many Christian interpreters have traditionally taken it). We need to read and understand Paul’s argument in the historical context of his day, which also requires that we appreciate the Hebraic background of the key (Greek) terms that Paul employed. A greater sensitivity to the orthodox Hebraic concepts underpining Paul’s terminology, and a greater understanding of how the Mosaic covenant actually functioned, would greatly aid the Christian church in understanding the genius of this great apostle of faith.