Serial killers have a well known profile; childhood abuse, playing with fire and torturing animals. Seems to strongly suggest serial killers are a product of nurture.
The playing with fire and torturing animals part isn't evidence for nurture, it's just evidence for the early stages of the same psychopathic behavior as the later serial killing.
It's true that many serial killers were severely abused and/or neglected as children. However, the fact that the overwhelming majority of people who were abused or neglected as kids don't grow up to be serial killers or other psychopathic criminals suggests that there's more going on than just a bad environment. Also, not all serial killers were abused as children, as I recall, Jeffrey Dahmer had emotionally distant and divorced parents but he was never abused in any way.