Many school districts have the rule that instructors/administration are not allowed to stop a fight due to that very reason Lil. Liability issues....
There have been many lawsuites against teachers/principals and school districts when the teacher waded into the fight to split up the kids. Parents then sued the school district because the kid was "injured" by the teacher splitting up the fight.
In school districts that violence is an everyday thing, many of them have hired special guards or even have off-duty police roam the hallways. In that aspect, those who are in those positions can break up a fight with no liability issues because they are "specially" trained to do so.
A fight recently broke out in our high school, and the teacher could only stand in the doorway after she called the principal. He called the police and 5 minutes later they showed up. In the meantime, both kids have bloody noses and the classroom was pretty much trashed by the other kids egging them on. In that instance, I wouldn't have had the ability to even try to break up that fight as the kids were pretty big, and fists were flying pretty fast.
One parent furiously asked why nobody broke up the fight and saved little "Johnny" from his beating...well, little "Johnny" was the one who started it...
So, sometimes it is damned if you do, and damned if you don't.