I've already explained why morality has to flow from conscience and can't can be proven with reason alone. So I'm not here to argue for Retribution. I'm here to refute a few of the common attempts to argue against it.

1: "Punishing people for their wrongdoings doesn't make them good people." (Perfect Solution Fallacy)

That's completely true. You know what else is true? Feeding starving orphans doesn't change the aspects of human nature that create poverty, so let's not do any of that either. You see? For any good action you can name another good objective that it doesn't accomplish. No action furthers every good objective. So just because there's one good thing punishing unrepentant criminals doesn't do doesn't excuse us from the duty to do it.

2: "Punishment is sometimes okay as a deterrent for future wrongdoings, but to do it just for the sake of some abstract idea of 'Justice' is pointlessly hurting people." (Circular)

You have a disputed assumption here that it's pointlessly hurting people. My claim is exactly that it's not pointless, so this argument is circular. Our real difference is one of axiology, which - see the above linked article - can't be logically refuted unless it can be shown to be internally inconsistent.

3: "Killing a murderer or being mean to someone for being mean is hypocrisy." (Circular, and hypocritical as well outside of full-on pacifism)

The principle behind my judgements is not "X is always wrong", but "doing X to an innocent person is wrong" (note that I still took out always because there's at least one other category of exceptions). This objection assumes that people who act differently should be treated the same, which is, of course, absurd and almost everyone knows it when you spell it out. What becomes clear the more you think about this is that the problem with people who make this argument is that they don't see any difference between good and evil. They only look at methods, ignoring goals and context. They think all meanness or all violence is the same; they think your allegiance is determined by your weapon.

And beyond that, does anyone think it's hypocrisy to fine a thief? If doing what is normally wrong becomes okay because the target did it first, what is the difference? The only person who can even make this objection without contradicting themselves is a pacifist.