The first incident which seems to demonstrate to Mr. Darcy that he and Elizabeth share similar personalities occurs when Elizabeth visits her ill sister Jane at Netherfield. In Chapter 8, as Caroline Bingley struggles to belittle Elizabeth in order to win Darcy's approval, the conversation turns to reading and "accomplished" young ladies. Elizabeth and Darcy banter back and forth about what makes someone accomplished, and Darcy appreciates Elizabeth's wit and intelligence. For once, instead of a woman pandering to him, he has met someone who challenges him.
In Chapter 34 of Pride and Prejudice, Mr. Darcy proposes to Elizabeth for the first time. After Elizabeth's angry response to his less than romantic declaration of love, Mr. Darcy writes a letter to Elizabeth to try to explain his behavior.
In Chapter 35, Elizabeth receives the letter which details Mr. Darcy's motives for treating Wickham as he does and the logic behind his disapproval of a match between Bingham and Elizabeth's sister Jane. In providing Elizabeth with the facts of the Wickham case, Darcy demonstrates that he knows that Elizabeth--like him--is a logical creature who demands evidence for someone's ill opinion of another. Moreover, although he does not admit to it in the letter, Darcy seems to recognize that he judged Jane too quickly just as Elizabeth was too hasty in her judgment of him.
Finally, it is not until Mr. Darcy proposes to Elizabeth the second time in Chapter 58, that he seems completely self aware of his own shortcomings which are ironically similar to Elizabeth's. He admits that just as her own mother and father have allowed their daughters to act as they please, his father spoiled him as the only son. He confesses to Elizabeth,
"By you I was properly humbled. I came to you without a doubt of my reception. You showed me how insufficient were all my pretensions to please a woman worthy of being pleased" (350).
At last, Darcy recognizes that he suffers from his own pride and prejudice which he had observed in and criticized Elizabeth for earlier in the novel.