Paul is speaking to Peter and the other believers who came from a Jewish background. When they came to recognize that Jesus of Nazareth is the Christ and put their trust in him for their justification, they thereby affirmed that man is not made righteous in God's sight through obedience to works of the law. They demonstrated this conviction by forsaking the old covenant purity laws, confident that Christ has cleansed all those who come to him (Hebrews 10:19–25; Ephesians 5:26–27). Now, by acting as if those laws are needed to be part of God’s people, they acted in a manner that is at odds with their own basic attitude.1
16 yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified.