as a boy growing up I was in my fair share of "squabbles". It is definitely a boy thing.
My parents never taught me to fight; to defend myself; yes, but not to fight. They based their instructions on the Christian motto - "turn the other cheek". As a result I was usually pummeled; and walked away to find a teacher to speak to . That action cost me the respect of my peers. The philosophy carried with me into adulthood and it took some tough experiences ( not fights) to teach me to be "assertive"---a very different perspective than being aggressive. And light years differnt then "turning the other cheek".
In response to this I have taught my son to fight back --not as an agressor--but as self defense. I think it is important for "the other kid" to know that the victim will "fight back" and inflict some damage. Most of the aggressive kids are bullies anyway, and will back down when they realize that they do not have a scared victim.
As for the school, they understand the difference between "picking a fight" and " self defense".
Frank