And what I'm saying is that the school administrator has a vested interest in "removing bullying" by making all bullying-related in incidents be actually something else.

I agree that violence is never the answer, but maybe next time instead of talking to someone who wants to not have to deal with bullying, talk to the students who are being bullied. I guarantee you that every single one of them has tried to alert an adult and the reaction was either "well he's not doing anything too bad so I can't do anything" or "he's been put in detention temporarily and I am the only one aware that it was related to bullying".

Every single instance of kids fighting in schools can be fixed by having actual support systems in place against bullying. Figure out who the bullies are, and remove them from the bullied's life. Treat bullying as we treat parental abuse currently, it should be unacceptable that a treacher knew what was happening and did nothing, yet it happens daily.

Fact: currently, if a kid is being is being bullied, they need to learn how to end a fight.

What exactly is a person of authority going to do of you go to them? If they are going to actually do anything, is that thing going to stop it? I guarantee it won't. Their rational might be this, but as it stands either you are blissfully unaware of the reality of bulling or you are aware and simply do not care.