One argument we hear against the death penalty goes like this: "So let me get this straight: you're saying murder is wrong, and must be punished with murder? Give me a break!"
Yes, I'm saying murder is wrong and must be punished. But is the punishment to be considered murder too? I don't think so.
Both the crime and the punishment involve taking a human life. But murder, by definition, is the taking of a life "under conditions specifically covered in law". So the taking of life in the second case is not murder. You may argue that the state is arrogating for itself certain rights which the citizen does not possess, but that's how government works.