The purpose of Paul's letter to the Galatians was to make it clear that becoming adopted descendants of Judah, nicknamed Jews, through circumcision offered to gentiles nothing in regard to salvation. Paul stated that even circumcised Jews had to be justified through the blood of Christ and afterwards live a Spirt-led life.
But the people of Galatia were either impressed or intimidated by the circumcision argument. They saw this as a reasonable way to change their ambiguous social identity as neither idolaters nor Jews.
Paul understood that this path of reasoning would have clouded the Galatians' understanding that justification is by the grace of God through faith in Christ's shed blood and the faithful obedience that comes through Christ's indwelling by the Holy Spirit.
Paul pointed out to the people that they did not need to be adopted by the Jews to become 'sons of God (Galatians 3:26) and receive eternal life.