At the first Meryton ball, Darcy refuses to dance with Elizabeth. Why does he refuse her, and why does she refuse his offer to dance at the next assembly?

Darcy is rather a snob. Darcy refuses to dance with Elizabeth saying, “she is tolerable, but not handsome enough to tempt me.” He goes on to say that he has no interest in women who are “slighted by other men.” Elizabeth finds Mr. Darcy pompus and a rich snob. She doesn't wish to dance with somebody who looks down on her.