1) you don't need to be a highly skilled operator for the gun to be effective. The fact that the teacher is armed... And all he/she knows is basic gun safety and doesn't even have the skills to use it.. if I was a potential shooter and I have that in the back of my head that the teachers are armed... I'd think twice before shooting up the place.
It's all about basic deterrence. A vulnerable target is more likely to be attacked than a target that looks formidable.
Same thing applies to bullying. The weaker looking ones get attacked more likely than the tougher looking ones. Why the weaker looking kid has to compensate by hitting the gym, callousing their knuckles via knuckle push ups... and learning how to effectively carry a numb facial expression to deter a bully.
I know because that's what I've done in school and presently at my workplace in order to deter potential bullies. Because I look weak. By default I look like a sissy boy. An easy target.
2). Missing the signs? Because people are generally self-absorbed in their own world that they fail to spot who is being ignored or isolated and such.
3). The school system is screwed up on so many levels. My major beef with it is it's political correctness that only serves to highlight each other's differences. Oh he's white! She's black! He's gay! Etc... It's divide and conquer and it forms people into cliques and puts them in an "us vs them" mindset creating hostility...