Paul instructed Titus to avoid foolish controversies and speculative debates because such discussions do not benefit the church's spiritual life. They distract from the most essential things of the Christian life. The focus should be on teaching sound doctrine and instructions on godly living. Controversial discussions that do not contribute to the building up of the body should be avoided; it takes wisdom and vigilance to remain focused.
Aside from avoiding discussions that lead to quarrels, Paul gave Titus clear instructions on how to deal with people who stir up division. The person who causes division may be teaching false doctrines contrary to what the apostles taught or causing division through their behavior. The bad behavior could come from a root of bitterness that poisons the listeners' minds, leading to church division or a falling away (Hebrews 12:15).