I just want to say that no matter what the cause, things will probably turn out all right. It sounds like a few of you are having the same problem and are really frustrated and scared. When I was a kid, I was the only among my siblings who had similar behaviors. I didn't hit myself, but starting around the age of 5 (my mom said just after I started Kindergarten, and she thinks in my case that my very cruel teacher was a big part of the problem) I would say things like "I wish I was dead," and even, "I want to kill you," or "I hope you die."
My parents were also AP, and given the unique nature of these behaviors, it took them a long time to sort out the best way to respond. We did end up getting some "family" therapy at one point, and I don't think we had the right therapist, but had we gone to someone else, I think it would have helped.
My dad always had an easier time handling the situation than my mom. My dad would usually say something simple to the effect of, "I'm sorry" (and he was very genuine about it), and then he would refuse to involve himself anymore in my private drama. In other words, he acknowledged my feelings to prevent escalation, and then he ignored my behavior so that he wouldn't feed into it. It wasn't a miracle cure, but looking back, over time it was the most helpful approach in terms of helping me learn to deal with my emotions. At the very least, it always did much more good than my mom's approach, which usually involved a variety of desperate acts, from trying to reason with me to trying to comfort me to getting angry at me and involving her feelings in my personal drama.
I would think that the best approach for each kid with this problem has got to be customized to fit the kid. For kids who are affected by allergies, obviously working on an alternative diet would be the first step to healing. For kids with anger-management problems, preventative behavior-shaping activities might work well.
No matter what, though, this too shall pass. Next time your kid starts acting like a crazed lunatic, just think of me