What does it mean to be an example of a Christian man, or a Christian woman? Paul shows Titus in today's passage.

Paul shows Titus the results of letting worldly culture into the church, and the kinds of people who will do it. They stand in contrast to the elders Paul introduces in the previous verses... instead they're like anti-elders; who have a devastating effect on the faith of the church if their teaching is left unchallenged.