Let's say we come up with the time and resources to purchase arms for, train, and arm tens of thousands of teachers across the country in reaction to recent events in hopes of saving lives in the case of such a future tragedy.
Now, one outcome is that a similar event occurs, a teacher has the right training, wherewithal, and psychological fortitude to retreive their firearm, and successfully put down the attacker without injuring any innocent bystanders. This is the outcome many people like to see as not only a good outcome, but also a likely scenario.
However, there are a myriad other outcomes from implementing such a scheme. And the more guns you insert into such a scheme, and the longer it is in place, the more likely any of these other scenarios are likely to occur.
1) An attack does occur, and a teacher does retreive their firearm. However, in the chaos, stress, and confusion, the teacher shoots and kills one or more children.
2) An attack occurs, and a teacher retrieves their firearm. However, as is likely, most people (particularly those not trained in law enforcement or the military) find they cannot shoot another human being - or are unlikely to be able to hit another human being. The attacker, whose weapon has jammed, proceeds to take the gun from the teacher, shoot her, and shoot several more children.
3) There is a break-in at the school, and a firearm is stolen, which is then used in a crime where someone is killed.
4) A weapon is accidentally left out, or the ability to access it is discovered by some children, who then accidentally kill another student on the playground.
Now, these are just a few possible scenarios, and there are many variations on these as well. If one of these were to occur, what would the reaction of the public be? There is no way to guarantee none of these scenarios occur, so can it be rationally justified to implement such a scheme? How many accidental deaths due to such a scheme would be an acceptable number in hopes of possibly preventing future deaths?