It blows my mind to see you downvoted for this most simple and straightforward ethical statement — justice and retribution are not the same, and the state should be in the business of justice.
From Plato to the Tao, Christianity and Buddhism, Reverend King and Gandhi, most careful thinkers about ethics, philosophy, and government over thousands of years have come to the same conclusion. The purposes of punishment are to remove a dangerous person from circulation, to make amends to victims, and to deter other potential offenders. Revenge does not enter into it.
Replies here are talking about how good revenge feels, and threatening mob violence if revenge isn’t granted, but consider that those responses are in a context where there is little justice already. We know in our society that injustice is not often punished, and that revenge (e.g., shooting a healthcare CEO) feels great. That is further proof of the importance of justice, not an argument for retribution.