When Elizabeth goes to check on her sister, Jane, who is sick at Netherfield, she has to spend most evenings in the company of Mr. Darcy, Mr. Bingley, and Bingley's two sisters. On one of these nights, Elizabeth and Darcy actually talk about pride, and she expresses her feeling that pride is a weakness that is worthy of ridicule. Darcy says,
"Yes, vanity is a weakness indeed. But pride— where there is a real superiority of mind, pride will be always under good regulation."
In other words, Darcy does not consider pride to be a weakness, and his pride—ironically—does not allow him to realize how arrogant and snobbish this makes him sound. Essentially, he thinks pride is just fine whenever a person actually has good reason to feel proud (i.e., they are actually superior). In so saying, he implies that he believes he is superior.
This is confirmed when Darcy proposes to Elizabeth, conveying "his sense of her inferiority—of its being a degradation."
He discusses her low family connections, even describing how he has struggled against himself to overcome his feelings for her. He suggests that he loves her against his own inclination, his own intelligence: it is clear that his pride is wounded by his feelings for her because he knows her to be so far beneath him socially. And, further, though "He spoke of apprehension and anxiety . . . his countenance expressed real security" that she would, indeed, return a favorable answer to his marriage proposal. His pride leads him to expect that she could never turn him down, even after he says these terrible things to her. The certainty he feels that his proposal will be accepted by her, a woman he insults even while he is proposing, irritates and insults her all the more.