It's got a genetic component, but the real issue is still, to my knowledge, clouded. A mere genetic correlation doesn't mean it's the straightforward cause. For instance, you might inherit a gene from your mother that regulates fetal development, and get a different dose of hormones in the womb. This could give you slightly different brain development, which is also correlated with left-handedness (specifically, spatial and verbal thinking are less hemisphere-specific among lefties).
My info could be dated, though. I got most of it from this very good book. By the way I'm a full-on lefty.
Well, some have pushed for a “left-hander’s syndrome” condition to explain away things over the last few decades.
As relating to this particular case, if the “homework” that was found in Danville is in fact J. J.’s, then he claims that the rage in his heart first began because his sixth grade teacher forced him to write lines over and over as a form of punishment—something particularly painful for left-handers to do due to the way that they write. In short, being raised in a harsh right-hander’s world oppressed him so much that he eventually was driven to murder.