The simple answer to your question is no.
Maltreatment doesn’t justify return maltreatment. The appropriate response to maltreatment is either distancing oneself from the perpetrator (when one is able), “calling” someone out on his behavior (pointing it out), and/or reporting it.
Apologizing in this scenario seems counterintuitive because the rebbi wronged him. However, two wrongs don’t make a right. You need to hold your son accountable for his behavior while, at the same time, insisting that the school hold their rebbeim accountable for theirs.
The verbal abuse and chutzpah that you describe both seem to stem from inappropriate ways of managing/expressing anger. However, although they both seem related, your son is in school to learn, whereas the rebbi was hired to teach. I would point this out to the school to remind them that Torah is a living Torah, something to be embodied in our every day lives, not just learned/taught from a book.