This guy is grateful for that way of thinking, Doc.
High schools - no
Colleges - yes, if the school permits it (most won't sadly) and the students have proper licenses/cc permit/training, absolutely.
The argument that if everyone had a gun, or at least more students were armed, is the most frequent argument I here from anti-gun restriction advocates after after mass shootings take place. Yet how do we deal with the possibility of crossfire and mistaken identity occurring if no one can tell who the original shooter was. If one guy pulls a gun, starts to fire and then several others do likewise attempting to asset, what's to stop them from misidentifying each other or being killed by the police?
The real answer is to have adequate and well trained security for most large public gatherings/schools etc. Ban or heavily restrict weapons that have are typically used in modern combat while trying to keep hunting weapons and guns mostly associating target shooting and other sports regulated; requiring some form of licensing, training etc Limit magazine capacity; enhance background checks and loopholes around waiting periods. Attempt to stop mentally ill people from getting hold of weapons as much as possible through legal means.
Not every tragedy is going to be averted unfortunately. A determined madman can do damage no matter what. Still I see no virtue in encouraging a culture of gun ownership as a magic pill to the problem of mass shootings. Responsible gun users who know how to react under pressure and follow appropriate procedures are better than every macho guy thinking he's going to be the next Rambo if and when there's an emergency.
What one does on one's own property is another matter entirely, private schools would fall into that area as well. However it's a terrible idea that sounds great in theory, but doesn't really stand up to scrutiny. I certainly support the second amendment and interpret it as a right to bear arms, but like all rights nothing are absolute in all circumstances. Oh and sorry for a long winded reply to your rather short post (that was basically just an image), but my point is generally addressed to this rather common argument.