There is no mention in Acts of Paul going to Crete, but verse 5 implies that Paul and Titus had visited there, presumably in the latter stages of Paul's life. Paul had started a work there, but Titus needed to finish it, and this involved appointing elders in each town, implying churches had been established in several places on the island. The church in the NT is never seen as something that is imposed upon a people from outside. Apostles did come and establish a church, for there is no other way that the church could grow, but the goal was that the church became independent and self-sustaining, though remaining linked to, and supporting, other churches.
The requirements of an elder are similar to those outlined in the letters to Timothy. A man's family life was a vital element of the qualifications. Indeed, in some ways, our everyday lives are the best indicator of our maturity, or otherwise, in Christ.
Having listed a number of qualities that we must not have, Paul goes on to the positive. Leaders are to be hospitable, lovers of what is good, self-controlled, godly and disciplined. He must also have a sincere faith, and be able to teach the faith, and able to recognise and rebuke erroneous teaching.
This ability to teach the truth and to oppose falsehood is vital. It is vital now and was vital then. Just as then, there are many who are "rebellious and full on meaningless talk". In Paul's day it was members of the circumcision group who were the major problem. There false teachings were not just a matter of one opinion against another, but had a destructive effect. Likewise today, those who teach unbiblical stuff on sexual morality are not just offering another opinion, another way of looking at things, but are pedalling poison.
Verse 12sums up the state that Crete was in and was known for! Paul sees the role of the gospel to come directly against the attitudes and ways of life on Crete. Similarly today, the gospel should present a challenge to society, we are not meant to go with the flow, for society is flowing in the wrong direction.
Paul does not mince his words about the false teachers. They might claim to know God, but in reality they know nothing.