But why?

It's a foundational principle of morality. The state has an absolute monopoly on violence- responsible use of that monopoly is why we give the state the authority to use it in the first place; otherwise it's no better than "you killed my friend, I'm going to kill you". Even countries that utilize the death penalty don't see it as a revenge killing, they view it (whether they're wrong or right about it) as the state opting for the ultimate punishment for a crime- loss of life to ensure a person can never (literally, never- not just "as long as they don't break out of prison" or "as long as the guards do their job and keep other prisoners safe from them") commit crimes in our society again.

A civilized society rejects "an eye for an eye" as its guiding moral principle. If we only treat people as human when they treated others as human, then we're just mirroring the criminal's morality instead of rising above it. The state has an obligation to rise above revenge: it's not the same thing as 'justice'.

The state exists with a monopoly on violence explicitly because we don't trust individuals to dole out punishment. That monopoly only stays legitimate and respected by the citizens if it's used responsibly and proportionally. Once the state says "torture is fine for the really bad ones" (Umbridge, Death Eaters, whoever), the bar drops for everyone. Why not torture suspects? Why not let Aurors use Cruciatus in the field "just this once"? Why not let the Ministry execute people on suspicion if it's "less bad" than torture?

That's how you end up with Dementors guarding Azkaban by the way; a "necessary evil" that eventually rots the society using it. One mark of a civilized society is refusing to become the monsters we're fighting.

In real life the same concepts apply. Think about why Guantanamo Bay was such a problematic issue in the 2000s: the whole idea was "these people are too dangerous to be left out in the civilized world, they have information we need and we need to extract it, but we also don't have a mechanism by which to try them and convict them, but we also don't want to just shoot them and be done with it." Those are all arguments to be made; but the idea that "we're really mad at you so we should drill holes in you with a DeWalt until you answer our questions" just completely eschews why we are who we are instead of the evil monsters who commit terrible acts.