Why does it say "Al Ta'an Kesil k'Ivalto"?
Rashi: If you will answer him with controversy, perhaps you will be like him.
Orchos Tzadikim (Sha'ar ha'Shetikah DH Mi): The Kesil is pained via the Chacham's silence, more than if he would have answered him.
Malbim: A Kesil does not guard the laws of Chachmah, for he is drawn after his desire, which opposes the laws of Chachmah. In order to put a veil on his face and defend his Nefesh, he casts doubts on the laws of Chachmah and Emunah. If one argues with him to refute his doubts, it will not help. Even though he knows the laws of Chachmah, he casts them aside due to his desires - "v'Iveles Kesilim Mirmah" (14:8). Even if the one who argues with him will arrange matters known via the senses, he will close his ears - "Lech mi'Neged l'Ish Kesil u'Val Yadata Sifsei Da'as" (14:7). I command you not to answer him in the way of argument.
How will you be like him?
Malbim #1: It will be as if also you are unsure, and seek to resolve the doubts.
Malbim #2: Do not answer him amidst fear that if you do not answer him, they will say that also you are a Kesil, and if you answer him, you will show Chachmah in the argument.