I am a teacher. You do not want to arm teachers, trust me on this.
Mental health and how it is diagnosed and treated is a huge issue in America. My school does a good job providing support services as well as identifying said students for professional consultation, and with a full time school psychologist plus an extensive student services team, I feel they are doing the best they can to identify and support students that may have some moderate to severe mental health issues.
I don't know much about guns. I've lived in one of the most urban populated areas in the us my whole life in a state that already has some gun control, which i feel is warranted being in such a densely populated area. You don't want people in the city to be able to carry a concealed weapon, and Chicago has done a decent job trying to prevent access to assault rifles. Most of my friends do have some kind of pistol or hunting rifle that they keep out of sight and locked, but I think this situation is completely different and is more about the state of mental health and how we treat and diagnose it than gun control.