I only remember one incident where a person armed with a gun stopped a killer. Happened fairly recently, in a church if memory serves.
Now I compare that one incident to the many where responsible people had their guns stolen by criminals who used them, right then or later, to commit violent crime.
And I come to the inevitable conclusion that the latter easily outweighs the former and would outweigh it even more if people carried guns into such settings.
The problem with the logic of the two of you is that you are taking crime statistics after people weren't allowed to buy guns or arm themselves, making a causal connection to increased crime afterward, and then translating that to mean that, in the classroom setting, professors being armed with guns will reduce nutbags coming in on a death wish and shooting up the place (either because the nutbag is scared of the possibility that the prof is armed or because the professor has the wherewithal to shoot the nutbag before he really gets going).
The errors in your logic (even assuming your facts to be correct) are just so monumentally huge and obvious that the fact that you don't see them without their being pointed out to you means that either you don't want to see the errors in logic (more likely) or can't see them (less likely).
Bottom line: if you think that kid at Va. Tech. or the guy up at NIU would have killed fewer people if some professors (may or may not be around at tha time) were armed, you are deluding yourselves on use of firearms in those situations. And, even if one or two might have been spared by a professor somehow getting to and firing his weapon at the bad guy, that number will be smushed by the number of people killed as a direct and indirect result of the professors arming themsevles to being with.