Despite his protestations to the contrary, he is mentally ill, because he is obsessed with a cause which blinds
his view of what's right and wrong. Mentally healthy people have empathy, compassion, and don't murder innocent people to make a point, no matter how zealous they are. One kind of  insanity is a distorted view of reality and an incapacity to put oneself in other peoples' shoes. It's horrifying when obsessionals act out their darkest revenge fantasies. And when they do, that's proof of their sickness. Punish them, we have to. But even in a situation like this, rehabilitation is preferable to murdering the murderer. We can't forgive him his actions despite his lack of self-awareness, but we can help him, at this early age, look at life, his and others, constructively...unless he's a psychopath, in which case transformation is extremely difficult and unlikely.