My concern about the idea comes from the straightforward statistics - accidental shootings are much, much more common than mass shootings. We had a deputy leave a gun unattended in a jacket in a school near here, a prosecutor do the same in the next county over. We've all heard the stories of kids who got Mom's gun out of her purse or Dad's gun out of the drawer and accidentally shot themselves/someone else. And frankly, I'm not sure a gun in the hands of most of the teachers I know would make anyone safer - teaching is a heavily female profession, after all, and virtually all mass shootings are carried out by men. The idea of a troubled student overpowering a smaller teacher doesn't seem all that far fetched, and is a concern I've heard from several teacher friends.
In our area, a third grader in a school setting put his finger on a police officer's trigger (in the school) and pulled it, discharging the weapon. Fortunately, no one was injured. But if teachers everywhere are "armed" how long before there's an accidental shooting that kills someone? I give it a couple of months.