He could just walk along outside until he sees an empty classroom and come through that window, then walk into a full classroom and shoot the teacher before there's even time to unholster a gun. And, meanwhile, if you've got a bunch of armed teachers, you're creating all sorts of opportunities for accidental shootings: jumpy teachers who hear a beaker fall in the neighboring classroom, think it's a gunman breaking in, and they shoot the first person they see emerge from the room. Or a teacher leaving a gun in her purse when she leaves the room briefly, and a kid grabs it, starts playing with it, and accidentally kills someone, or a kid losing his shit and wrestling a gun away from a teacher and then going on a shooting spree. Etc.
Remember, the average number of school shootings per year is around 36. Most of those occur in ones or twos, not sprees where maybe an armed teacher can cut things short. So, at best, what are you saving? A dozen lives per year? And how many more are you going to be losing if you're flooding the schools with poorly trained armed teachers? It wouldn't take much to be a net loss.