The wisdom of the book of Proverbs is unparalleled. A simple placing of two apparently contradicting statements contain more practical guidance for this life than the best of life orientation lectures.
Answer not a fool according to his folly,
lest you be like him yourself.
Answer a fool according to his folly,
lest he be wise in his own eyes.
When should you answer a critic, and when should you respectfully excuse yourself and let the critic be? According to these two verses, the wise thing is to consider who would be the greater influence in the debate.
If, as the first proverb indicates, engaging a critic is only going to result in you resorting to the same tactics as the critic, then it is not worth the debate.
But, if, as the second proverb indicates, engaging the critic will cause him to reconsider his views in light of the Truth you are able to present, then go right ahead with the maturity, grace, and wisdom of God’s Word.
Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect.