Resisting False Brothers
Gal 2:3-5 Yet not even Titus, who was with me, was compelled to be circumcised, even though he was a Greek. This matter arose because some false brothers had infiltrated our ranks to spy on the freedom we have in Christ Jesus and to make us slaves. We did not give in to them for a moment, so that the truth of the gospel might remain with you.
Now if Titus were to be convince by the false teachers, indeed Paul would have run in vain, having wasted his time discipling that guy. But in fact these false teachers had no power, no influence, no effect at all in the private meeting. Their argument was completely uncompelling and had no effect on Paul's presentation of the gospel. They were powerless. Often bad theology is just not scrutinize because it's propagated solely through popularity. Remove the popularity issue, examine it in private, and alot of bad theology just falls apart and indeed often ends up looking quite foolish.
Another interesting thing about these verses is that here he speaks of "false brothers". Notice the parallel section in Acts 15:5 where it says, "Then some of the believers who belonged to the party of the Pharisees stood up and said, 'The Gentiles must be circumcised and required to obey the law of Moses.'" In Acts they are called "believers" because Luke is writing in an historical sense of their public affiliation, whereas Paul called them "false brothers", identifying their actual status. So throughout history to this day there are those who associate themselves with the Christian community, they are referred to as "Christians" or "believers", they may even hold positions of leadership in a church, and yet are false brothers. This was the case in the early church.