I've always believed that two wrongs never make a right. It's a repetitive cycle. If a person murders one or multiple people, yes they are a bad person and should be taken from society - preferably in solitary confinement for life with no human interaction - which believe me is worse than death. But if you're killing someone because they broke the law, and as it's usually for murder, then that doesn't make you any better than them.
Killing someone because they did something cruel makes you just as bad if not worst than the person who did something wrong in the first place. What is the point of that? It will not make the bad person undo what they did, but now you would have created a tragedy for no reason.
Human nature may desire revenge, but part of the purpose of society is to help us overcome our baser instincts. If all actions can be repaid with something equally cruel, there would be no end to the repayment. Justice systems must be set up to enact rules of punishment and rehabilitation that allow society to keep order in humane and rational way.