No & yes .. sorry if thats confusing! i believe sometimes childern are born with it and sometimes not. some kids may develope psychotic issues from there parents or surroundings and go Psycho and possibly going on a killing rampage.
But other than that your not born with it. ( hope that possibly made sense i tried my best )
A natural born killer is a good and interesting concept because it honestly depends on the surroundings, and the feelings they have. If a child is angry toward a parent, or a sibling constantly, they may go outside and i don’t know maybe kill a bird. Killing animals constantly out of rage or just spite is one of the main signs of that killing a person could be possible in that person. no one is born a killer, there are a lot of physiological aspects behind the motivation of killing . It depends on ur back ground, and u mental state