Paul makes heavy use of the Old Testament throughout this section, probably to combat how the Judaizers were mistreating it. Verse 10 quotes Deut. 30:15, v11 quotes Habakkuk 2:4, and v13 quotes Deut. 21:23, all to highlight the primacy of faith over the Law. In v15-20 he turns again to Abraham, noting that it’s through his seed (Jesus) that the promise of universal blessing would be fulfilled. This promise came from God directly, whereas the Law was given through intermediaries (angels and Moses), and therefore the Law does not overwrite the promise. Verse 20 cryptically states “but God is one.” This is shorthand for the standard Law-introducing formula from Deut. 6:4-5 and Mark 12:29-31.
Mirroring several passages in Romans, Paul teaches that the Law is about accountability, giving knowledge of sin. In that sense, it literally increases our transgressions! So we find that although the Law is good, holy, and God-breathed, it is not what saves us, but what condemns us. Its primary function, then, was to teach God’s people how hopelessly enslaved they were to sin so that when the Messiah came, they’d understand that their righteousness would come from him – from God.