Supporters of the death penalty: Can one of you please explain to me why you would ever need to kill someone?

I understand if we're talking about a supervillain that no prison can hold, but as far as I know, we're not having any difficulty with horrendous criminals repeatedly escaping. If we're fully capable of preventing a criminal from committing a crime ever again, why would we need to kill that person?

Does it make the victim's family feel better? If it does, should we be feeding that cruel and primitive need for vengeance?

It is potentially cheaper to just kill them, but in reality, it is known to be more expensive.

Is it a deterrent? Does the rate of capital crimes in an area go up if they outlaw the death penalty? I doubt it.

Before any of you say, "Why would we keep the criminal alive?" I would say that the burden of proof is on changing the status quo. You need a reason to kill someone. What is that reason?

EDIT: The death penalty is by definition tantamount to saying that someone does not deserve to live. Therefore, the fact that someone does not deserve to live is a judgment and not a reason. You can't say that someone deserves the death penalty because they don't deserve to live. That's like saying I'm bad at chess because I'm not good at playing the game of chess. It is true, but it is circular and contains no new information.