To the Torah, the first source of Judeo-Christian values, murder is the great sin; the immoral shedding of human blood (as opposed to the moral shedding of human blood in self-defense or in a just war) pollutes the world. That is why the Torah legislated that even an animal that killed a human should be put to death. The purpose was not to punish the animal -- animals do not have free choice, hence cannot be morally culpable. And it was hardly to teach other animals not to kill. It was because a human life is so valuable, it cannot be taken without the taker losing its life.
But, some will object, the Torah decrees the death penalty for many infractions, yet we don't put to death people who practice witchcraft, commit adultery or other capital infractions -- why those who murder?
There are two answers.
First, the only capital crime mentioned before there were any Jews or Israel (in Genesis when God creates the world) is murder. Other death penalties applied specifically to the people of Israel when they entered the Land of Israel -- a special code of behavior for a special time in a special place. And virtually none of those were carried out. The primary purpose of declaring a sin worthy of capital punishment was not actually to execute the sinner, but to declare how serious the infraction was when a society was establishing itself as the first based on ethical monotheism. Capital punishment for murder, on the other hand, was obviously intended for all time and for all people -- it is independent of the existence of Jews and declared to be fundamental to the existence of a humane order.
Second, all the other death penalties are laws. The death penalty for murder is not only a law; it is a value. Laws may be time bound. Values are eternal. Thus, the Christians who believe in the divinity of the Torah are not bound to the Torah's dietary laws (such as not eating pork and shellfish); but they are bound to the value of taking the life of murderers.
Finally, the Old Testament is preoccupied with justice. And allowing one who has unjustly deprived another person of life to keep his own is the ultimate injustice.
There are many good reasons to be wary of taking the lives of murderers -- such as insufficient evidence, corrupted witnesses, distinguishing between premeditated murder and a crime of passion -- but love of life or a commitment to biblically based values are not among them.