My dd has been a bully.
I have had another parent scream at her and also scream at me. According to that other parent, my dd was a horrendous bully.
The truth was far more complex.
The other girl was doing a lot of low level unpleasant stuff to dd. Calling her names, and being unkind. Nothing big enough to complain about, and nothing big enough for teachers to take seriously, and my dd wouldn't tell anyway. It really upset dd, and she reacted by bottling up and then being nasty. Mostly she was nasty verbally, but there were a couple of times when there was a push and shove between them, and twice when it was hitting.
I spent ages with both dd and school trying to sort it. I accepted that dd's behaviour was not right and that there was a string of incidents involving the other girl. The other mum would not accept that there was an issue on both sides, or that her dd had done anything at all, and she would not engage with school over it, and plastered all over FB that my dd was bullying her daughter. The head had to ban her from the playground after she screamed in dd's face.
The thing is, on several occasions I know her dd was lying. There was one time when her ds told her dd that my dd had hurt him in the playground. The school investigated and my dd had been in the library all break helping to tidy it. She wasn't in the playground. But her dd went home and told her mum my dd had done it.
There was the time she screamed at me about my dd doing things to her dd on the way home from school, except that, due to her saying there were problems, my dd no longer walked home from school alone. Yet she was still reporting incidents that could not have happened. Her dd was telling her they happened.
That mum was really, really upset with my dd and if you asked her, she would genuinely say that my dd was bullying.
I did everything school asked me to do, to make sure that dd did not behave badly, left this girl alone and that there were no opportunities for anything to happen (like picking her up from school). She wa spunished at home, and talked to at home. We tried to get to the bottom of it and we put action plans in place etc etc etc.
It got to the point at the beginning of year 6 where the class teacher agreed to keep them apart at all times so there was zero interaction. That worked, except her dd would still come over and try to play with mine. My dd was eventually allowed to walk to school again, one day her dd knocks on the door and asks if they can walk together! (I said no)
The thing is, I know dd was at least 50% to blame, maybe more. I know she was bullying. I also know that it wasn't 100% her fault.
DD is also poor at social skills. Her friendship skills are poor. She has had support all through school to try and help her understand social interaction better.
She is now secondary, and friednship issues are rearing their heads again, in a different form, not bullying, but this time dd is struggling to make and keep friends.
I suspect sh may be on the autistic spectrum, but she isn't 'bad enough' to get a diagnosis.
I think your OP is incredibly simplistic.
I am an ex teacher, and bullying happens for all sorts of reasons. It is rarely as simple as one kid is the bully.
The issue is always how a school deals with it.