This question already has an answer here:
The three unforgivable curses are the Cruciatus Curse, the Imperius Curse, and the Killing Curse ("Avada Kedavra").
The Cruciatus Curse inflicts terrible pain and has no use other than torture, making it understandably horrific.
The Imperius Curse overrides a person's free will and controls them directly. Again, understandably horrific.
The Killing Curse... kills the target instantly and painlessly. It's unblock-able, meaning it can't be deflected by a shield onto an innocent bystander, and it's implicitly single-target-only, with no explosion or similar splash effect which could cause collateral damage.
On the other hand, all of the following are apparently perfectly forgivable:
- The Blasting Curse, with huge potential for collateral damage, and which could cause severe injury leading to a prolonged and painful death.
- The Expulsion Curse, similar to the above.
- Whatever was used to blast Benjy Fenwick to pieces, possibly one of the above.
- Nonspecific Dementor-associated death after imprisonment in Azkaban (eg. Morfin Gaunt) (Not just condoned, but practically enabled by the authorities)
- Sectumsempra (inflicts horrible wounds which, if untreated, could easily lead to slow death by exsanguination)
- Whichever curse afflicted Dumbledore after wearing Marvolo Gaunt's ring (I don't think it was ever named).
There are also countless other ways to potentially kill someone with magic (Body-binding curse-assisted drowning, for example). In light of all of these "forgivable curses", why is a safe, instant, painless kill so horrifying as to be "unforgivable"?