Everybody has the right to life.
If it is wrong for someone to kill, then it is equally wrong for the state, which after all is composed of individuals, including you and I, to kill too.
If the state is government of the people, by the people, for the people, then the people are killing the culprit.
Also they are doing it in our name!
An eye for an eye, and a tooth for a tooth, means just that, After all it also says, "Though shalt not kill"