We read:
“For the grace of God has appeared, bringing salvation to all people.
It trains us to reject godless ways and worldly desires and to live self-controlled, upright, and godly lives in the present age, as we wait for the happy fulfillment of our hope in the glorious appearing of our great God and Savior, Jesus Christ.
He gave himself for us to set us free from every kind of lawlessness and to purify for himself a people who are truly his, who are eager to do good.
So communicate these things with the sort of exhortation or rebuke that carries full authority. Don’t let anyone look down on you.” Titus 2:11-15 NET
I note in the NET translators note; they mention: (All men as generic, referring to both men and woman) {Paraphrased}. This is also based on the Greek.
Q: So what does Titus 2:11 mean in relation to “the grace of God has appeared, bringing salvation to all people”?
I’m not convinced of Universalism, yet this sounds very general. For example: True believers are saved by grace through faith (Eph 2:5,8,9).
False believers are distinguished from the true as being condemned, & liars, see: (1 John 2:3-4, Matthew 7:21-23)