What is the comparison to a dog that returns to eat its vomit?
Yuma 86b #1: This is one who confesses again what he already confessed and repented from it.
Yuma 86b #2: This is one who sinned and repeated the sin - it becomes permitted in his eyes.
Sha'arei Teshuvah 1:4: A dog eats repulsive things, and when it vomits them, they are more repulsive, and it returns to eat them. So a Kesil, when he does a lowly act, and repeats it, it is more lowly.
Malbim: After explaining what to answer a Kesil, disgracefully with light matters, it explains why one should not answer him with Chachmah, in the way of argument. It is because he repeats his folly, like a dog returns to eat its vomit. It is bad food that he cannot bear it, and vomited it. Even so, it swallows it again. So a Kesil repeats the folly that he 'vomited'. He knows that it is despised - he knows that there is no substance to his folly and doubts - "v'Iveles Kesilim Mirmah" (14:8).
