How else do you describe the premeditated taking of another person's life? What is murder if not that? Ah, that's right, only bad guys can murder. If a good guy does something bad, you can just call it something else and it's all good. By all means support it all you want, just don't delude yourself into thinking it's some sort of tasteful, modern practice of justice.
This.
It's state controlled murder. The whole point of the western justice system is a balance between punishment and the right to appeal if a perceived injustice has been done. Execution is finite; a person in life imprisonment for the most henious of crimes can appeal his sentence and if found innocent can be made free. An executed man cannot.