At the beginning of the novel, their relationship starts off on bad footing when Elizabeth is introduced to Darcy at a ball, and she deems him aloof, snobby and quite rude, as she overhears some of his rather condescending comments about her and her family. Darcy is intrigued by Elizabeth, but doesn't give her much thought. Later, as they are put into more situations together, their relationship grows in complexity. Elizabeth walks over to Bingley's house to check on her sister Jane, who is there ill. Darcy is again intrigued by her rather unconventional approach, and likes her forthright opinions and self-confidence. Elizabeth, however, still thinks that he is snobby, and her opinion of him worsens as Wickham spreads lies about Darcy's past relationship with him. Then, when Elizabeth finds out that Darcy discouraged Bingley's attachment to Jane, her bad opinion grows even more. But Darcy is so interested in her that even offers a proposal, which she rejects.
So, Elizabeth, for a good portion of the novel, thinks that Darcy is a haughty, arrogant and cruel person. She is incredibly prejudiced against him, and prideful in her attitude. After the first proposal rejection, Darcy sees that Elizabeth can be quite snobby herself, and that her family has some tragic flaws that are pretty hard to overlook, especially after the Lydia/Wickham elopement. Elizabeth, on the other hand, starts to soften her opinion of Darcy; she learns the truth of Wickham's nature, and realizes that Darcy was prudent to warn Bingley of their family. She sees his estate, and hears reports of his amiable and giving nature, and she even has several positive experiences with him and her aunt and uncle. She learns to love him, and regret her rejection of his proposal.
So, both characters are hindered by both pride and prejudice at different parts of the novel, but eventually learn to overcome them and develop true and deep feelings for one another. I hope that helps; good luck!
Becasue he see that she not after his money. Also, that she like to bechallenge by someone who is not dum and can but up a challenge. And learn things off each other. Mr. Darcy starts to see thing in Lizzy and as time goes their love starts to grow as well. Then they fall in love.