Paul called some supposed believers false, saying they were not Christians. They did not understand or truly accept the good news about Jesus, unlike the apostles in Jerusalem (2:3).
had come in under false pretenses: Paul suggests that a larger group of Jewish "Christians" opposed his preaching (see Acts 15:5) and supported the false teachers who joined the church.
Requiring non-Jewish Christians to follow Jewish law would trap them in rules and deny the good news of Jesus (see Galatians 3:23–4:11).