Why exactly is the Avada Kedavra unforgivable?

Hey guys. Here's my question. Why is the AK an unforgivable curse? Sure, it's death, but why is it "unforgivable"? It can't simply just be death because you can also kill people by slashing them with a curse etc but those aren't "unforgivable curses".

In the graveyard when Harry is fighting Voldemort (Triwizard tournament), Voldemort is using the wand with which he killed Harry's parents (important information). Eventually their "spirits" come out of the wand to help Harry escape. In that context, here's my theory:

Avada Kedavra is an unforgivable curse because it doesn't just kill someone, it also steals their soul and entraps it in the wand, making the murdered person unable to move on to the afterlife. It's the ultimate cruelty - it ties the soul of the deceased to the murderer's wand, entraping them forever.

What do you think ? Does it make sense ?

And if you share my theory, do you think that destroying the wand could release the souls and "save" them ?