A murderer can be a person who killed in self defence all the way down to one who kills for fun or greed. The motivation matters very much. One is acting from a sense of love, the other is emotionally indifferent and cruel. These are very different neurologies and should result in very different responses from society.
The murderer has a story to tell. Is is the story of a hero, a protector, or the story of the greedy? Are they a person or a zombie, a good-heart or a rotter?
When a person is evil, when they kill from a sick addiction, when they are cold and cruel, for the state to murder them is a form of euthanasia. Execution is murder too. Killing is killing.
The murderer is a tool of evil, an arm extension of demons.
In a world that encourages the development of the prefrontal cortex over the primitive drive, a proper love-nexus, there would be far few murderers. Our environment effects brain development. How much empathy, logic and self control we have matters.