After all, Moses had been given the Ten Commandments by God on how to live. The Bible, the Old Testament had at its heart the Torah, the Law. It was through the Law that God showed his love for a particular people, the Chosen People, Israel. Jesus himself was one of the Chosen People. Now, along come these gentiles from Antioch who want to become disciples of Jesus.
Gentiles eat food sacrificed to idols.
Gentiles attend feasts of fertility gods, which was nothing more than a way to find justification for sexual immorality. If gentiles were to become true followers of Jesus, it just made sense that they should follow Jewish practices and Jewish laws. Or at least, that's how their argument went. But then the other side gave their arguments led by Paul and Barnabas. Of course the Gentiles should not practice sexual immorality, but they also should not be expected to follow all of the laws of the Torah.