Is "Av" literally his father?
Rashi #1: No, it is Hashem.
Rashi #2: Yes.
Why does he gladden particularly his father?
R. Yonah: He recognizes his son's Chachmah, and knows whenever his son speaks Chachmah.
Malbim: The son gathered the laws of Chachmah, and conducts according to them. This is a son that his father taught to him the way of Chachmah and Musar.
Why does he grieve particularly his mother?
Rashi: He is constantly in the house with his mother, and she sees his lunacy, and is pained.
Rashi (according to the Mashal): The verse discusses a son like Yaravam ben Nevat; he grieves his assembly.
Malbim: A Kesil is cast off from the way of Chachmah due to his desire. She draws him close. Therefore, the good is attributed to his father, and the evil to his mother. The father teaches Musar; the mother longs for her son, and does not let the father chastise him with a staff.
Why do the verses discuss Kesil, Rasha (2) and Evvel (8)?
R. Yonah: All are adjectives for one who does evil deeds.
