I'd disagree that they are all society's products. There must be a proportion who are just born fucked up, otherwise there would have been a fundamental shift in the specific sicknesses of the core group of scumbags. By that I mean, that while each time has it's killers d'heure, which are no doubt made by that which surrounds them[1], there is a long running line of rapists, and yer basic no-regard-for-life killers of opporunity. Where all fuckups a product of society, there would not be a running thread of identical behavior, but rather a more dynamic and evolving history os assholes, as we find with the first subset described above.
[1] It may be argued as well, though I do not know how convincingly, that this group of people would actually turn out bad in any society, but with specifics drawn from that environment.
As to the death penalty......
Premise A:
Killers are evil, and should be punished.
Premise B:
The death penalty is a just way to remove those who murder.
Premise C: Execution is the just killing of the guilty.
Premise D: Murder is unjust the killing of the innocent.
Premise E: execution is carried out by the state in the name, and with the specific consent of, the people.
Conclusion, if just one innocent human has been fried, paralysed or gassed in your state, you are a murderer and should be executed, no ifs, ands or buts.