Verses 15-21 may represent the continuation of Paul’s confrontation with Peter, or it may represent a statement of the central point of his letter: that Christians are justified by faith in Jesus Christ alone.
In verses 15-17, Paul is not denying that those who are Jews by birth are sinners, as are all Gentiles (rom 3:23). Rather, he is implying that Jews enjoy spiritual privileges (Rom 9:4-5) that should make them more knowledgeable about how to be justified before God (3:6; Gen 15:6). The Jews should have been more aware that no person could be declared righteous or justified by obedience to the Law of Moses (3:10-21).
Verse 16 is one of the most important verses in Galatians because in it Paul states the content of the gospel of grace. This is the first time Paul uses the word justified which means “to declare righteous.” Justification is the act of God, whereby He declares the believing sinner righteous in Jesus Christ.
In verse 21, Paul presents a brilliant conclusion. The very reason Christ died on the cross to pay for sin was because the law could not remove sin or impart righteousness. Grace provides what the law was powerless to provide—righteousness.
The simplest way to look at this section is that verses 15-16 are the transition to the content of the Gospel, while verses 17-21 show that grace does not promote sin.