Even assuming the premise of killing someone implies mental illness, and assuming the mental illness stems from trauma, there's a pretty large leap in reasoning here. Why must the trauma come during childhood? Why not in adulthood? Even in childhood, why does it have to come from the parents?
Then you have the idea of continuing up the causal chain. Why are we pressing charges to the parents? If the parent's traumatized their kids, there's good chance they did it due to their own mental illness/trauma, which means the parents themselves were abused in childhood. So we should go after their parents.... except that just means we should go after there parents.... ad infinitum.
People that kill other people often function well in their society. It doesn't make sense to me to classify that as mental issues. People are inherently territorial, aggressive animals - at least to the extent being so doesn't make them much of an outlier.
Is that even true?