15 We who are Jews by nature, and not sinners of the Gentiles,
16 knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.
we who are Jews (v.15) — Paul reminded Peter of their shared heritage
Jews (v.15) — originally those of the tribe of Judah, but now, and here, used for the race of Israel as opposed to Gentiles.
by nature (v.15) — by origin, not by conversion
sinners of the Gentiles (v.15) — Paul uses the terminology of the Judaizers who despised Gentiles in order, in the next verses (v.17), to show that the Jews are equally guilty of sin.
The Jews did form a holy nation and had inherited the covenants and promises of God. They had attained a certain sanctity in contrast with sinful Gentiles. Paul reasons from this fact, and he turns against the Judaizers their familiar language. He declares that in spite of all their privileges and regardless of their arrogant pretensions to superior holiness, even Jews, even man like Peter and Paul, had found that they could not be justified by works of the law, and had been compelled to turn to Christ for salvation. If, then, even Jews could not be justified by their attempt at keeping the law, why bind the law upon Gentiles who had been saved, like Jewish believers, by faith in Christ? — The Epistle of Paul to the Galatians, by Charles R. Erdman, page 52-53.
knowing (v.16) — understanding the truth of the gospel
a man (v.16) — any human, Jew or Gentile
justified (v.16) — declared to be right, righteous before God.
is not justified (dikaioo) = to show, or declare, to be right (Luke 7:29; 10:29; 1 Corinthians 4:4). In the majority of its New Testament occurrences dikaioo = "to declare a person to be righteous before God," All doers of the law are justified (Romans 2:13), with this proviso, that if a man "shall keep the whole law, and yet stumble in one point, he is guilty of all" (James 2:10; Galatians 3:10). As a matter of fact, however, no such doers of law have yet been found among men, and "there is no distinction," i.e., as between Jew and Gentile, "for all have sinned, and fall short of the glory of God," i.e., fail to secure the approval of the sole Lawgiver and Judge. Clearly, then, by works of law shall no flesh be justified or accounted righteous, in His sight (Romans 3:22-23), the conclusion here, as in the more extended argument of the Epistle to the Romans. And this the converted Jews had themselves acknowledged when they sought justification through Christ. — Galatians, by W.E. Vine, page 165.
works of the law (v.16) Hebrews 6:1; 9:14. Law is the Mosaic law, but, by extension, any law — so — Nobody, Jew or Gentile, has ever been declared righteous by God based on his obedience to law.
even we (v.16) — Jews
for (v.16) = because — followed by a paraphrase of Psalm 143:2 — Do not enter into judgment with Your servant, for in Your sight no one living is righteous.
no flesh (v.16) — no human, with the emphasis on "no."
faith in Christ (v.16) — should be "faith of Christ." The character that makes Him worthy of our faith. Our faith in Christ is effective because of the faith (faithfulness/worthiness) of Christ.
… The life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself for me (Galatians 2:20).
How believers need to learn this blessed truth! We are kept, while in the flesh, not by "our faith" but by His faithfulness. Our God-given faith is but the channel through which we appreciate and enjoy His never-failing faithfulness.
Our "faith" would be vain were it not for "the faith (fidelity) of the Son of God." The best of us would utterly fail were it not that "He ever liveth to make intercession for us" (Hebrews 7:25) and "now appears in the presence of God for us" (Hebrews 9:24). — Studies in Galatians, by Cornelius R. Stam, page 133.
Verses 15-21 are probably part of what Paul said to Peter at Antioch.