As someone who has had every insult and defamation hurled my way ( i also do not have any children) by bratty children, i agree with the posters that under no circumstances can a rebbe take personal feelings to heart or make decisions based on them. When i write recommendations, i go by set criteria, not how the boy made me feel. Honestly, kids are mean and it’s happened to me (and every other rebbe i know!) that kids will ask mechilah years later for all the horrible, sometimes unthinkable things that they say and do.
I don’t know if the rebbe needs to ask mechila though; the kid needed a severe punishment for such a deliberately hurtful thing to do; same punishment should have been given if the boy said it to a different rebbe, or any other adult. Honestly, if things were the way they should be, I’d punish kids for things they do outside school if i found out about it, but administrations don’t believe in that for some reason. A rebbes place isn’t just a classroom; you’re supposed to train children for their lives, not just to sit still for a few hours and then be animals.