Talking of course of the relationship between Elizabeth and Mrs Bennet...Jane Austen does not exactly explain why Elizabeth is the girl with whom Mrs B gets on worst.

That Lydia is a favourite, we all know why; Catherine probably follows close behind since her temper is rather similar to Lydia's; Jane is beautiful and likely to make a good match due to her beauty and sweetness.

That leaves Mary and Lizzie.

Why is Lizzie even less dear to her mother than Mary, whose pursuits she would be unable to understand?

I see 2 main reasons (remember that this assertion of JA is made before Lizzie's rejection of Mr Collins which will later add a 3rd one):

1) Lizzie is her father's favourite, and the relationship between Mr and Mrs B is at least tense... Though I am under the impression that usually Mr B simply ignores his wife and does not often wilfully confront her (except when marriage questions are at stake).