The devil knows how to ask foolish questions. The first introduction to him shows him asking Eve a foolish question. There is no reason to question anything that God says. The devil is a liar and a murderer from the beginning. Sadly, all people are deceived by him at some point.
Titus also needed to avoid genealogies. It is interesting to know some of the history of ones ancestors, but it is foolish to waste a lot of time looking back and trying to connect families. God stated that those who are saved should avoid this empty pursuit. Natural families are not as important as spiritual families. The sad reality is that many families will be separated at death because most do not want to know the truth. There will be few that will be saved.
Contentions involve quarrelling. We know that the Jews were involved in quarrels about whether there is a resurrection or not. They disputed other teachings that Paul gave as well. The Bible is the truth. It is important to know the truth and teach the truth. When I was in Bible School we were told we needed to have debates on certain topics in one of my classes. I cannot remember the topic I was assigned. I needed to choose which side I wanted to take. I refused to argue for the wrong side, just to have a debate. It is a waste of time to play ‘devil’s advocate’. Some people are attracted to debates but God says we should avoid contentions. It is important to teach the truth and not waste time arguing with those who do not want to know the truth.
Titus also needed to avoid strivings about the law. In Matthew 19 the Pharisees came to Jesus tempting Him. They wanted to know if it was right to divorce a woman for every cause. They came to Him with the wrong question. There were two basic “schools” of thought among the people on divorce. They were trying to trap Jesus into one of those two “schools”. Jesus avoided that temptation by taking them back to the beginning. God’s law cancelled out both of those humanistic “laws”. The truth is indisputable. It is the truth and everything else is a lie.
Paul stated that getting involved in the aforementioned events is unprofitable and vain. Some time back I was asked to debate the issue of Bible versions without using the Bible. I told the person involved that there was no point in doing so. The Bible is the Word of God and I am not interested in seeing if there is some merit in the perversions. There is no value to them at all and I know that and am not interested in wasting time in a humanistic argument. Someone might be a better debater and have all kinds of information on their pet peeve, but that information might all be wrong. They are convinced it is right and arguing on the basis of human thought is unprofitable. The truth is what matters and God’s Word is truth.
In verse 10 Paul gave instructions regarding an heretick. A heretick is someone who holds to false doctrine and insists on teaching that. Calvinists are hereticks. They hold to false doctrine and they want to promote that false doctrine. The Charismatics are also hereticks. There are many others that fit into that camp. God says we need to seek to show them they are wrong, but there is a limit to how much effort we should put into that. You notice as well that Titus was not to debate hereticks. He was to admonish them. To admonish is to rebuke. False doctrine has no legitimacy. It is false and needs to be rejected. Those who want to hold to false doctrine need to be exposed. We have often warned of the danger of New Evangelicalism. I was raised in that trash. As an adult I was involved in that lie. God delivered me from it and I have no interest in getting back into it. It concerns me when I see others getting involved in that lie. I refuse to attend a New Evangelical service, unless maybe for a funeral of a relative. If I attend such a funeral, I will look for opportunities to warn those in attendance of the fallacy of what they teach and believe.
Those who are truly born again are often taught to be far too passive regarding false teaching. They don’t want a ‘fight’ so they compromise just to get along. That is in fact a New Evangelical concept. Those who are saved are not looking for a fight. We are simply seeking to obey the words of Jude 3.

Jude 1:3 Beloved, when I gave all diligence to write unto you of the common salvation, it was needful for me to write unto you, and exhort you that ye should earnestly contend for the faith which was once delivered unto the saints.

John the Baptist refused to accept the false teaching of the Pharisees. He exposed them for their heresy. Jesus Christ exposed the false teachers during His earthly ministry. Paul did the same.

Ephesians 5:11 And have no fellowship with the unfruitful works of darkness, but rather reprove them.