They were just low ranking teachers and the students they were teaching are either from a wealthy family or from a poor family. They were not allowed to interfere into any fight because of the past incidents that had occured in the academy.
The incident almost caused a full scale war between the neighborhood. It almost made all magical creatures stopped their children from going to the academy, but they knew a greater problem awaits them if they don't. Then the teachers had a meeting with the parents and they finally reached an agreement. The parents had to set up a rule that no teacher must interfere into the student's fight. They were in a world where each person must fight for himself. So it's best if the students gets to fight and settle disputes among themselves.
They all agreed on this decision and the parents turned the mage academy into the survival of the fittest.