lbibliophile:

Just like Slughorn, Albus Dumbledore collects people. Only, instead of focusing on those with influence, he looks to the outcasts.

The expelled half-giant.
The young werewolf.
The repentant Death Eater.

He protects them and gives them a second chance. All he asks in return is their loyalty.

And, if on occasion he requests that they undertake a certain task, invoking their debt of gratitude – well, that is no more than he is owed.

He once thought to add a certain disowned Black to his collection, but quickly realised his mistake.

Sirius is not an outcast, but a rebel. He knowingly chose his path, and chooses what price he is willing to pay for it. He refuses to be used.

So Albus Dumbledore abandons him.