Killing serial killers is tantamount to putting down rabid animals.
A serial killer can be removed from society and prevented from having an opportunity to kill. “Putting him down” is just you stooping to his level out of misguided self-righteousness
A rabid animal is suffering from the final hours of a horrible communicable disease that is 100% fatal. It’s in horrible pain, out of its mind, and you are doing a mercy to end its misery