While it is true that Mrs. Bennet does not favor Elizabeth over her other daughters,
Lizzy is not a bit better than the others; and I am sure she is not half so handsome as Jane, nor half so good humoured as Lydia.
it is also true that she has at least the general interest that her daughters can be married off well prior to the death of Mr. Bennet.
While this latter event is not likely to happen anytime soon, the reality of the Miss Bennets is that, according to the law of their time, the estate that belongs to Mr. Bennet has to be entailed to the next male in his family line, hence making this person his heir. This means that the Bennet sisters would be at the mercy of whoever the heir is, upon the death of Mr. Bennet. A situation that illustrates this sad event can be found in Jane Austen's Sense and Sensibility, where the Dashwood sisters are, in fact, disenfranchised both physically and socially by their half brother, John, who is the male heir to which their father's estate is entailed.
Back to Pride and Prejudice, since the heir to the Bennet estate is Mr. Collins (and since he shows interest in Elizabeth), Mrs. Bennet would naturally jump at the possibility of making an arrangement where not only would Elizabeth marry a man of good income, but also become the duly "heiress" of her own estate through marriage.
This dry and calculating method of courtship may seem primitive and weird to the modern reader but, during Austen's time, women were quite limited socially, financially, and even academically. To have a good income meant the possibility of a bigger dowry (a down payment, sort of, to procure a good husband), and hence a bigger chance to succeed socially.
Therefore, Mrs. Bennet is in no way a mother who demonstrates a warm devotion to Elizabeth, but she certainly hopes the best for every one of her daughters (even Mary!).
Personally when i read this book i felt that she didnt really care about Lizzy at all. Her main aim was to get the daughters married regardless if they like the person at all. She wanted Lizzy to get married so they can inherit any land and money
Elizabeth was Mrs Bennet's least favourite child so she wanted Elizabeth to marry Mr Collins as he was going to inherit LoungBourn property.