"because I killed a kid I gotta kill everyone" WHATTT????

It is not about him killing the kid, but that he was forced to kill the kid by humanity and their greed.
Oh turned his child into an experiment, making him fight jin lee. The whole of this story showed Jin Lee encountering the depravity, self-interest and consequent results of humanity. He is fed up with being stabbed in the back, used, endangered and being a danger. so he plans to end it all.
At least that is my take

ohhhh see now that makes sense