I can see both sides of this argument.
On one hand, if a man just murdered your entire family and the cat, you'll want them dead. It's part of human society. We're a naturally warlike species. And if someone did this murdering in cold blood, yeah, they might be a deranged psychopath (by definition, not just a crazy murderer) and unfit to be a part of society.
Then again, being a psychopath doesn't mean that you want to kill people. some psychologists argue that psychopathy is just the effect of a brain that works in a far different way to the general public, and if they become criminals or not depends on their upbringing.
So, back to the other argument, wishing someone dead after they killed someone you know is natural, but everyone knows Hammurabi's Code, and this reaction is a blinding of logic. Punishment usually means that you are teaching somebody else a lesson, be it the criminal, or other criminals seeing the public hanging in ye oulde times, they won't want to touch a weapon or stolen goods for a while after. However, some people don't take these cues, and continue with their practice.
However, a life sentence could be worse than a lethal injection, because you'd live in poor conditions, surrounded by other criminals (who might be in for worse than you are), and they might kill you with sharpened spoons. Or you'd die of old age and organ failure, if you're lucky.
So, what would be less painful: Death by spoon, or death by fast-acting toxin?