Elizabeth is both beautiful and smart, but she is not that easy to marry off. She is offended by her mother, and her mother is frustrated because she does not understand her daughter.
It is not so much that Mrs. Bennet does not like her daughter as that her daughter frustrates her, and she frustrates her daughter. She just wants all of her girls to marry a nice rich gentleman from a good family, to save the family fortune.
The greatest conflict between Elizabeth and her mother is that Elizabeth does not want to marry Mr. Darcy. Mrs. Bennet desperately wants one of her daughters to marry well, so they don’t lose their land because the family has no sons.
Both sisters were uncomfortable enough. Each felt for the other, and of course for themselves; and their mother talked on of her dislike of Mr. Darcy, and her resolution to be civil to him only as Mr. Bingley's friend, without being heard by either of them. (ch 53, etext p. 185)
Ultimately, Elizabeth does accept Darcy’s marriage proposal, but only because she has come to accept him and appreciate him, and even understand him.
I'm not sure I would say Elizabeth is the least favorite daughter.. but I think Elizabeth has very little in common with her mother in terms of interests and temperaments. Elizabeth has little regard for the petty thrills of society that preoccupy Mrs. Bennet.