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If you want an interesting killer that breaks the mold look into Ed Kemper. He wasn't born evil. He was made evil by his mother.
He projected his disdain for his mother onto many poor innocent victims of the university his mother worked for. He'd be coined the "coed killer" and would later kill his mother as his finale.
After he killed his mother he turned himself into the police and was pretty much completely rehabilitated.
He now resides in prison at the ripe age of 73. He's asked multiple times to be put to death and is said to be the nicest guy you'll ever meet.
Kemper is a good case for nurture being just as much a factor as nature if not more important.
Had he not been abused by his mother then he wouldn't have needed to kill in the first place. No need to displace emotions he never experienced. His after the fact behavior is 100% different than you would expect. He's an incredibly smart, kind and respectful man.