Problem: Paul writes, “For the grace of God has appeared, bringing salvation to all men” (Titus 2:11). Does this passage teach that everyone will be saved in the end?
Solution: To make a claim about systematic theology (such as universalism), we need to consider the Bible’s full, systematic teaching on this subject. When we consider the Bible’s complete teaching on the fate of the lost, we find that sadly some people will freely choose to be separate from the love of God. For comments on universalism see Colossians 1:20.
In this passage, the statement could be rendered to all men or for all men. Hiebert comments, “The adjective rendered ‘that brings salvation’ (sōtērios) asserts its saving efficacy. The dative ‘to all men’ may equally be rendered ‘for all men,’ thus stressing the universality of the salvation provided. Salvation is available to all, but its saving effect is dependent on the personal response of faith.”
 Hiebert, D. E. (1981). Titus. In F. E. Gaebelein (Ed.), The Expositor’s Bible Commentary: Ephesians through Philemon (Vol. 11, p. 440). Grand Rapids, MI: Zondervan Publishing House.