As a Neurology student with extensive background of general biology I might have some answers. It's very difficult to understand the cause and mechanism of Aspergers Syndrome because it has strong genetic influences and is quite paradoxical. However, I meticulously searched out advanced sources on the internet, and between that and observing the behaviors of Aspies I know personally, I think I can paint a broader picture of Aspergers, particularly in regard to mass shooters.
It's foolish to think that Aspies don't have the capability and/or intent/will to commit harm. I am going to argue, based on from what I know, that people with Aspergers actually have very low cognitive and emotional empathy. It's got less to do with morality and more to do with ability. Aspies have above average connectivity (synapses between neurons) which overwhelms the neurons with constant signals, that's why they have extreme sensitivity and because of that they usually seem to be disassociative and avoidant to cruelty and malice, not because they are truly good compassionate people but because they simply get overwhelmed. On the surface they seem to have virtuous or just philosophies, but that's because with their already hypertensive state of mind they can't afford to invest in other people's endeavors.
The strange thing is unlike neurotypicals and sociopaths they use their frontal lobes rather than the limbic system to intellectually deduce what the other person feels, rather than just doing it instinctively and quickly like we do. In that regards they seem colder than sociopaths but their neurological methods of socializing are inferior and inefficient. They behave superficially politely or compassionately, since it's better for them to avoid confrontation. The thing is, the hyperconnectivity can go both ways: they can experience above average intense stimulations that explains their obsessive narrow behaviors and because they are so hypertensive they can even experience pleasure more intensely (in certain activities) and theres no reason to think that these activities can't involve downright cruel aggression and sadism. Contrary to popular belief, Aspies have the potential to be even more cruel than sociopaths; Lanza and Elliot Rodgers certainly experienced great pleasure in killing those people.
You have ubiquitous comments from Cassandras who date Aspie men saying things like "But he's so nice and gentle, the other day he walked an old grandma across the street," and "he treats animals nicely," however this is actually misleading.
Aspies, as I mentioned, don't use the necessary parts of the lymbic system in the midbrain region like we do for social communication; instead they use the frontal lobes, where logical thinking and concrete reasoning works, therefore they have a very technical, pedantic, robotic awareness of social norms. Aspies usually try hard to please people and try to follow every moral, social and ethical convention. They also lie less because they want to avoid conflict and confrontation because to them it's the path of least resistance. However, neurologically speaking, this is actually just selfishness: they don't do these good deeds to help people, but rather to make themselves socially presentable.
Like schizoids, they are scared to be judged, confronted, and criticized.
I don't necessarily agree with everything this commenter said. For instance, I'm still not convinced that Adam Lanza and Elliot Rodgers took the same kind of pleasure in their killings that, say, a Ted Bundy did. But the description of the over-connectivity in an Aspie brain was new to me and made perfect sense: much of their behavior is a defense against overstimulation. I've witnessed that myself, and have heard Aspies cry out, "Too much chaos!" if two people are doing different things in a room at the same time. And they are bothered by, for instance, television commercials, in a way that NT's never are. And if anybody even jokingly pretends to be cruel, Aspies will lecture them about their "morality."
And his description of their "technical, pedantic, robotic awareness of social norms" was right on target as well.