While I do believe that this is a pretty bad policy and one of the stupider ones I've heard of - equally, the contention that bringing armed security (i.e. guns) into schools is somehow not a valid solution isn't a sensible one either.
If you have a situation where armed people are targeting schools, I don't see how armed guards are going to make that situation worse rather than better. There are armed marshals on planes, armed guards at airports, in many countries there are armed guards at banks and jewelry shops. What exactly is the problem with armed guards at schools?
Absolutely, arming teachers is an absurd idea, though.