Almost every kid goes through a period (or even periods) in their teenage years where they feel unloved and unwanted. I'll go out on a limb here and say that this is a product of their environment (the being unloved bit) not their warped psychopathic minds. Mostly this environment improves (new friends or finally leave school and hang out with adults, whatever). Sometimes there can seem no end to the environmental causes of this "adolescent depression" (for the kid in middle of it anyway).
Sometimes they end up in such pain they take their own lives.
Often the child has identified the elements in their environment causing them pain (correctly or incorrectly). It seems that in some cases they decide to do society a favour (in their minds) by removing these elements (in this case killing the people at their school who hated them) as well as themselves.

That's what I think anyway.

john