What does 1 Timothy 1:4 mean?
Paul has specifically asked Timothy to remain in Ephesus in order to combat inaccurate doctrines. Two serious problems with the false teachers in Ephesus are myths and genealogies.In this context, "myths" are traditions not found in the Scriptures, which add to or contradict biblical teaching. Not all traditions are bad, but those which conflict with God's Word certainly are. Discussing these myths is one thing, but far worse is to be devoted to them.
The idea of genealogies connects with Pharisaical tradition. Jewish religious leaders prided themselves on having a family heritage connected to Abraham or some other important Jewish forefather. Genealogies are important in Scripture, but are not part of making a person more holy in the eyes of God. In Christ, Jews and Gentiles who believed became one family based on the work of Jesus rather than works of the law. This was why Paul could write he was, "a teacher of the Gentiles in faith and truth" (1 Timothy 2:7).
Peter had dealt with the controversy of Gentiles coming to faith in Christ much earlier (Acts 10). In Acts 15, approximately AD 50, the Jerusalem church and its leaders decided not to impose the Jewish laws upon Gentile Christians, urging them to follow a few areas of practice while acknowledging the importance of the Torah.