Kyle was never actually prone to the act of killing someone. It was just that he was greedy to become stronger.
He didn't want to live the same life as in the past before the old universe succumbed to its fate.
Kyle hated his past life to the core, or the end, at the very least.
Things were not supposed to repeat themselves and to prevent this, Kyle had to start killing, the more the better.
More kills mean more souls, which meant that it was possible for him to become stronger at a much faster pace.
The system behind his Nurture ability was simple, and the fastest way to become stronger was to use the overlapping effects that were created by combining his special trait of possessing a Spirit Soul, and the Nurture ability.
Thus, slowly as time passed, Kyle had accustomed to killing, the more the merrier.