So here's another one for you. I get dispatched to a school shooting as a cop. I'm one of the first few guys into the place. We hear shooting coming vaguely from a part of the school and we move that way. As we're moving down the south hallways on the main floor, Mr O'Grady, the late twenties teacher in the tech department who had no class that period, comes out of a doorway with his gun drawn also moving towards the sound of the shooting, with kids running down the hallway towards him and us. I move to the sound of shooting and in doing so I see an adult male emerge from a classroom with a gun up and kids in the immediate vicinity.
Worst case, police shoot and kill a teacher. Best case, the first contact team is now stuck in a high risk takedown because they saw a person with a gun, and now because they're dealing with that individual they lose several minutes of time where we could be stopping the *actual* threat, but we think we may be dealing with either the or another suspect.
Even if teachers were to become armed, they had better hunker down in a classroom covering kids. If they go armed into the hallways they are putting themselves at huge risk and hindering the police response because we will be unable in those critical few minutes to differentiate the teacher from the shooter.