"Correct a mocker and you will gain an enemy"
So what is a mocker? One definition to consider is that the one who rejects Christ is a mocker, one who disdains the teaching of Christ to the point of refusing to submit to the Son of God. Anyone who has heard the Gospel and yet rejected it would be such a person, an unbeliever.
And so, back to our proverb here:
Correct a Christ-rejector with Christian morality, advice, instruction, guidance, etc., and you will gain an enemy.
Jesus put it this way,
"Do not cast your pearls before pigs nor give what is holy to the dogs lest they turn on you and tear you to pieces."
As a pig has no appreciation for the value of a pearl, and like a dog who has no appreciation for something holy, so a Christ-rejector has no appreciation for the treasures of wisdom and knowledge which come through Christ. Such treasures are spiritually discerned and appreciated but the unspiritual person simply lacks the sense for it.