IF the teacher is armed, who does the gunman shoot first? After the teacher is shot, then what?
As already noted, nothing is going to stop a shooter from emptying a mag or two into a class. Things will happen too fast for most to have an effective response. However, armed teachers can mitigate the damage, keeping it to a lower amount. Sure, a teacher in a given class may be shot first, but then you have the other armed teachers on location and in close proximity.
I don't think any of these answers are as practically effective as they are a deterrent. The current system of "Gun Free Zone" is ridiculous and promotes school shootings.
I don't know that guns have been particularly effective deterring crime. They have been helpful in fighting crime, but bad people continue to act, undeterred.
Your assessment that folks shoot in "gun free zones" isn't because they are gun free necessarily. They shoot there because they have high concentrations of targets.
You have also confused cause and effect. "Gun free zones" don't promote shootings. They may fail to prevent shootings, but that is NOT the same thing as promoting shootings. It is a semantic issue, but semantics are critical when it comes to properly understanding problems.
These cowardly shooters aren't looking for a gunfight, they are looking for power and revenge.
I always like it when we resort to calling bad guys "cowards" because the bad guys show up more prepared than the good guys. The notion of starting off with more power and buy surprise isn't cowardly per se, but an effective strategy. It is used as a military tactic to overwhelm the opposition.
Whether or not the bad guy is brave or a coward isn't really an issue. In the cases of recent school shootings, most are planning on being dead at the culmination anyway, so it isn't a matter of being brave or cowardly, but how much havoc and damage they can reak. Getting sidetracked by name calling and trying to feel superior by putting down the opposition is an excellent example of how we underestimate the opposition.