It's about evaluating risks. There is a risk that a crazy violent person will create an elaborate plan for mass slaughter and chose to target your place of work or your school. There is also a risk that someone, who is otherwise non-violent, will make a terrible decision in the heat of the moment. A few dozen people die each year in spree killings. Many thousands more die in shootings and suicides.
While it's possible that an armed teacher might help reduce the carnage of a spree killing, trained armed security on site didn't stop Columbine. There are close to 100,000 public schools in the USA. If you introduce weapons to that many situations, do you really think the risk of tragedy goes down?
Again, Adam Lanza's mother had multiple weapons. It didn't afford her any protection. In fact it led directly to her death and that of many others.