In Titus 1:9, we are told to know our faith well so that we can encourage and to correct those who oppose the truth (It is not about opposing us.). We are the products of our what we believe and value. Wrong belief will leads to wrong decisions and to wrong living and ending with bad consequences.
The people who believe wrongly will teach others to believe wrongly as well. Hence any wrong believe must be stopped ( Tit 1:11). We are told (v13) to rebuke them sharply that they may be sound in faith. "Sharply" is not in emotional manner (angrily, fiercely, ..) but in accurate and sound arguments. The purpose is for them to have "sound" faith for living well. How can we do that unless we ourselves are also sound in our faith. The proper way is Kindness 1st then Truth 2nd.
It is imperative that we dig in the Bible in depth, and ask the Holy Spirit to be our teacher and guide, check the original Hebrew and Greek words, and compare the teachings and commentaries that we may come across, and organized 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.