There's a legal dimension to arming teachers that I haven't seen discussed. The law privileges the police to use deadly force. But it also permits police officers to use deadly force under ambiguous circumstances, and to make mistakes - sometimes serious ones - when they shoot.
The basic 4th Am. standard for a reasonable use of deadly force that applies to officers would presumably apply to teachers. (Though states could enact statutory constraints, etc.)
The lines are especially hard when other people also are armed. For example: Police rolled up on an armed man who had done "nothing illegal." Before they arrived, one officer told the other"Fuck it, shoot him." And they did. 8th Cir. said this was a reasonable use of force. 
Another example: Police approach the house of an "innocent young man" in the middle of the night. He answers the door, carrying a gun lawfully and is shot and killed. 11th Cir. said this was close enough that the officers enjoyed immunity. 
And those are just the cases in which the officers actually knew that the person they shot was armed. But courts have also said it was reasonable for the police to shoot people who were holding phones or reaching for wallets, because police mistakenly thought they were armed.
Another example: Last year, the 11th Cir. said it was reasonable for the police to shoot an unarmed man because - in the space of about 3 seconds - he held his wallet in the wrong way. 
Courts have set the reasonable-force line where it is in part because of the realization that officers must sometimes make "split-second" decisions about whether to shoot someone. And it acknowledges a trade-off - police are sometimes allowed to shoot people unnecessarily. 
So the question is whether we would be willing to permit a similar trade-off in schools.
One other data point worth keeping in mind: Per @washingtonpost's tracking, police officers fatally shot 68 unarmed people in 2017, and 26 people who had toy weapons.
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