Every commentary I’ve heard on the shooting has been predicated on the idea that it’s impossible to empathize with the emotions behind his actions. Maybe I’m projecting, but I believe it’s all a bunch of social posturing meant to deflect suspicion. I’m writing this in a public place and it’s pretty damn intimidating to see someone peek at that title over my shoulder.
Have you never felt anger or rage to the point that you’ve wanted to kill someone? Anyone? Have you never had a revenge fantasy? And I’m talking aside from the drugs Lanza was on, the autism, and the other confounding variables. I’m talking about a core component to the human experience. Everyone experiences similar emotions in kind*, if not perhaps in such mind-warping magnitude.
Maybe it’s just obvious to me because I stand perennially closer to the abyss. I’ve spent days on end looking into the darkness. Statistically, it’s nigh impossible that I’m the only one who’s dropped a pebble out of morbid curiosity, just to listen to the sounds. Maybe I’ve dropped a couple of them.
[Edit: Seriousness aside, it’s a lot easier to understand this emotion just now, as I’m being subjected without consent to perhaps the 500th rendition of Jingle Bells I’ve heard this year. Ohh, they really jazzed it up! What a crazy idea!]
[Edit 2: I’d forgotten that someone made a movie about this idea, and it was one of the very few that I saw this year. It’s called Chronicle, and I think it bombed. MovieBob did a spoiler-riffic job of reviewing it, if you just want the jist of.]
*Aside from the confounding factors, as I mentioned.
Aeoli Pera 
The dude killed kindergartners he never met. When most people get angry, they try to take out the source of anger. Or at least don’t kill kindergartners they never met.
In another possibility, “I understand” is too close to “I agree with” for most. Rational people try to distance themselves from psychopaths.
The pebble example reminded me of “Eyes of the Dragon”.
But it’s silly for everyone to act like evil is inscrutable. It’s not. Just for instance, there’s an obvious psychological link between this guy, his mother, and her surrogate children. See how easy it is to make connections when I don’t pretend I’m so pure and righteous that I “could never understand”?