You have to feel it.
Severus Snape stared into the eyes of the man he had looked up to, the man he had always turned to when he was at his most desperate.
The Unforgivable's couldn't be cast without the caster putting their whole self into it. In the case of the Killing Curse, you had to want the person dead, had to need it, more than life itself. Little wonder the Dark Lord was mad.

He looked into Albus Dumbledore's pleading blue eyes, knowing, in some deep, visceral way that this was the last time he would ever do so.

Curse the man. How dare he make Severus do this? All to save Draco Malfoy's precious soul.
(He never would have tried this hard for Severus. He needed Severus to be his little spy- traitors have no innocence.)
He sneered.

"Severus. Please."
At that moment he hated the old man, possibly more than he had ever hated Potter, or even the Dark Lord himself.
He raised his wand, pointing it straight at the old man's chest.
"Avada Kedavra!"

And in that moment, watching the body of Albus Percival Wulfric Brian Dumbledore tumbling from the tower like so much damage, his piercing blue eyes dimmed forever by his own hand, Severus Snape understood why such a magic was deemed Unforgivable.
For in the moment of passion, he had committed a crime so terrible most mortal minds would crack under the strain and he knew that, whatever the old man had said, there would be no refuge, no escape, from the truth-he was a murderer.
Irredeemable- unforgivable. Now and forever.

-
Finally uploaded this. Very sorry to anyone waiting for an update of Partners In Crime- real life is a bitch.