Sirius claims that he doesn't see the world in black and white. He recognizes that Dolores Umbridge doesn’t have to be a Death Eater to be evil. But when it comes to Snape, Sirius isn’t quite as perceptive. He just can’t believe that Professor Snape, who was once a Death Eater, could ever be one of the good guys . J.K. Rowling points out this contradiction in Sirius's character:
Sirius is very good at spouting bits of excellent personal philosophy, but he does not always live up to them. For instance, he says in "Goblet of Fire" that if you want to know what a man is really like, 'look at how he treats his inferiors, not his equals.' But Sirius loathes Kreacher, the house-elf he has inherited, and treats him with nothing but contempt. Similarly, Sirius claims that nobody is wholly good or wholly evil, and yet the way he acts towards Snape suggests that he cannot conceive of any latent good qualities there. Of course, these double standards exist in most of us; we might know how we ought to behave, but actually doing it is a different matter! (source)
Sirius's own inconsistency is proof of what he is saying: Sirius is a good man, but he has bad sides to his character. His complete inability to forgive Professor Snape or to move on from childhood rivalries indicates his own enduring and dangerous immaturity.