I think it is both. People are born with some genetic dispositions or something mentally not right. Whether or not that turns into serial killer material all depends on the upbringing. A game of can we catch the signs soon enough. As my sociology teacher said "Video games don't make kids violent, but they can show us red flag behavior if we pay attention". Example of ed flag behavior: Obsession, violent lash outs, inability to separate fantasy from reality, glee in killing things (yeah sim players make me worry). There is also the point that a killer of animals will one day will turn on humans.
The trouble lies in neglectful/abusive parents who don't pay enough to their children. Or parents who are just-what do I want to use... They see the signs but blow it off or blame it on other things. Or the age old boys will be boys. So as these issues with personality and behavior arise no one corrects them and the behavior continues until sometimes escalation.
I understand a lot of serial killers were the "quiet boy next door you never suspect" but when their families talk about their childhood it's littered with red flags.
Fun fact: A lot of serial killers had yellow rooms as kids.