It's been pretty obvious to humans for the last few thousand years, probably longer, that burning hatred is the primary cause of violence, not lack of empathy. Why have so many people recently forgotten this? Why do so many people assume that someone is likely to randomly commit an act of violence without external stimulus, simply because they don't care? In order for a person to have the capacity to hate someone, they have to be able to relate to them on a human level to some extent, therefore have some level of empathy. For example, a lot of people with Schizoid Personality Disorder are incapable of hatred because they lack the ability to relate to people as other human beings, therefore they have no motivation to commit acts of violence.
All this stuff about violence and lack of empathy is probably related to the tragedy at Sandy Hook, because Adam Lanza had Asperger's, and Asperger's is often associated with lack of empathy. We can't completely lack empathy though, otherwise we'd be a lot more like people with Schizoid Personality Disorder. I guess that's as deep as the media wanted to dig for a convincing stereotype. It worked anyway though, because they succeeded in making it look like lack of empathy can be the primary cause for someone to commit an act of violence. But it can't, it either has to be caused by an external stimulus such something provoking anger, or an internal stimulus related to psychosis. A lot of animals probably don't feel any empathy towards me, but they don't randomly attack me for no reason. Why would a person who feels no empathy towards me randomly attack me for no reason either?