If this guy was genuinely concerned he would run for office instead of pontificating on the Internet. It's funny that as mentally unstable as school shooters are they never seen shoot up a police station or an NRA convention. Why do you think that is?
I see your "reasoning" there, but it fails upon actually viewing what is being proposed.
Yes, shooters seldom shoot up places where trained gun-bearing individuals congregate for obvious reasons. But it does not follow that arming teachers will make things better. First off: you can't demand that one of the primary skills of being a kindergarten teacher is that you need to be a military trained marksman; it just won't happen. Secondly adding guns to an already gun-laden society doesn't seem to have EVER improved the situation. As more guns get in circulation more bad actors get access to guns just statistically.
The idea of dousing a gasoline fire by pouring more gasoline on it doesn't seem like a great idea and has absolutely zero evidence that it would work. Meanwhile much stricter gun laws DO show evidence all over the globe.