Tit 1:9b that he may be able by sound doctrine both to exhort and to refute the opposition.
In Titus 1:9, we are told to know our faith well so that we can encourage and correct those who oppose the truth (It is not about opposing us.). We are the products of what we believe and value. Wrong beliefs will lead to wrong decisions and to wrong living ending with bad consequences.
The people who believe wrongly will teach others to believe wrongly as well. Hence any wrong belief must be stopped ( Tit 1:11). We are told (v13) to rebuke them sharply so that they may be sound in faith. "Sharply" is not in an emotional manner (angrily, fiercely, ..) but with accurate and sound arguments. The purpose is for them to have "sound" faith in living well. How can we do that unless we are also sound in our faith? The proper way is Kindness 1st then Truth 2nd.
It is imperative that we dig into the Bible in-depth, and ask the Holy Spirit to be our teacher and guide, check the original Hebrew and Greek words, compare the teachings and commentaries that we may come across, and organize our knowledge of the faith, jotting down our misunderstanding and clarification and those that need further exploration. It is with effort that we may truly grasp the truth, live in it, and by it, that we may lead the abundant life promised in John 10:10 and touch others as well.
