Titus 2:15

The apostle closes the chapter (as he began it) with a summary direction to Titus upon the whole, in which we have the matter and manner of ministers' teaching, and a special instruction to Titus in reference to himself. I. The matter of ministers' teaching: These thing, namely, those before mentioned: not Jewish fables and traditions, but the truths and duties of the gospel, of avoiding sin, and living soberly, righteously, and godly, in this present world. Observe, Ministers in their preaching must keep close to the word of God. If any man speak, let him speak as the oracles of God, Pe1 4:11, and not the figments and inventions of his own brain. II. The manner; by doctrine, and exhortation, and reproof with all authority. Ti2 3:16, All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, and for instruction in righteousness; that is, to teach sound doctrine, to convince of sin and refute error, to reform the life, and to carry forward in what is just and good; that the man of God (the Christian or minister) may be perfect, thoroughly furnished to all good works that are to be practised by himself or to be taught to others. Here is what will furnish for all parts of his duty, and the right discharge of them. "These things speak, or teach; shun not to declare the whole counsel of God.

— Matthew Henry's Concise Commentary (public domain)

with all authority--Translate, "authoritativeness" (compare "sharply," Tit 1:13). Let no man despise thee--Speak with such vigor as to command respect (Ti1 4:12). Warn them with such authority that no one may think himself above (so the Greek literally) the need of admonition [TITTMANN, Greek Synonyms of the New Testament]. Next: Titus Chapter 3

— Jamieson-Fausset-Brown Commentary (public domain)