What probably happens is a teacher would misplace or improperly secure their firearm in the school, a student would get a hold of it and then start shooting. Every gun in a school is a huge risk to prevent a (relatively) infrequent problem.

Plus, let’s say it goes as planned. An armed gunman enters the school and starts shooting people. Some of the teachers grab their pistols and start looking for the shooter, some of the teachers barricade themselves and their students in their classrooms and guard the door with their gun. The teachers roaming the hallways have only a basic description and location of the shooter, every student and staff member they encounter is a split second decision about life and death, the chances they don’t shoot innocent people and actually shoot the perp before they get shot is extremely low. Now the cops show up. Not only do they have an active shooter, they now have multiple armed individuals roaming the halls that they have to apprehend, but only one of them is actually the shooter. What are the chances all those teachers surrender and disarm quickly, quietly and without injury? You also have multiple barricaded rooms with armed defenders to clear, oh, and there is still a shooter on the loose.

It’s fucking stupid. No one with a working brain who has actually been in a public school would think that arming the staff is the correct response.