Scriptural and traditional authority
Some readers of biblical and other religious texts understand certain passages as permitting or requiring execution for grave offenses. Others interpret those passages as historical legal material rather than a rule for modern states.
Justice and proportionality
Some people view execution as a proportionate response to intentional killing, particularly when they believe the harm is exceptionally severe.
Deterrence
Supporters argue that the possibility of execution may discourage lethal violence. Evidence about deterrence is contested, and conclusions depend on how studies define and compare crime rates.