Retribution
First a reminder of the basic argument behind retribution and punishment:
all guilty people deserve to be punished
only guilty people deserve to be punished
guilty people deserve to be punished in proportion to the severity of their crime
This argument states that real justice requires people to suffer for their wrongdoing, and to suffer in a way appropriate for the crime. Each criminal should get what their crime deserves and in the case of a murderer what their crime deserves is death.