The relationship between Elizabeth Bennett and her mother might be characterized as a reversal of the roles of parent and child. Both women are portrayed as headstrong and incapable of persuasion by the other, but their temperaments, aims, and understanding of the nuances of the social world they inhabit are completely at odds. By all accounts, Mrs. Bennet is a woman of limited experience and tact. She is single-minded in her purpose: Seeing to it that all of her daughters are married off to well-endowed men, regardless of the characters of those men.
Elizabeth, by contrast, is quite independent in her thought, more refined in her bearing and far more circumpsect than her mother about the impression she is making on others. Throughout the novel, she sees her mother as a great source of shame and embarassment, hindering her attempts at heading off the antagonisms of the Bingley sisters, who take delight in the crude nature of her kin, and ingratiating herself with Darcy.
There is a great tension between what Mrs. Bennett desires for her daughter and what Elizabeth herself desires, and the two are irreconciably at odds with one another on this point. The sense that one gets of the relationship between the two is that it is Mrs. Bennett who is the child, sulking in petulance when things do not go as she intends, speaking whatever crudity may come through her head at the present moment regardless of who hears it, running to her husband to try and get her way. Elizabeth, when she is not seething at her mother's indelicacies around good company, treats her as both a vexation and simultaneously as a source of amusement. Her mother in many respects behaves as though she were an overgrown infant and her daughter has taken on the role of the sensible adult in the room.
While this tension is not the focus of the novel and ultimately does not irreparable tarnish the relationship, it gives the reader the sense early on that Elizabeth has been tethered unwillingly to someone obstinant, whom no amount of earnest entreaty or other tactic can persuade, and who, if left unchecked, will spoil her chances at living a meaningful life. Mrs. Bennett seeks to mold Elizabeth in the only mold she knows, as she has done with her younger daughters, who have dutifully carried on the legacy of her frivolity. There is an underlying antagonism between mother and daughter that, if not resolved, has potentially grave outcomes for one or the other.
This tension between Elizabeth and her mother is pertinent in light of the theme of Pride and Prejudice. The novel at its core is about the way we rely on our first impressions of others to form our opinions and guide our actions. Elizabeth's ability to make a favorable first impression, to show off her individual talents and personality, is constrained by her mother's claim to her as her progeny and as an instrument to be used in crafting her own image to present to the world, that of a successful mother whose daughters have all married well. This competition of wills highlights the absurdity of relying upon first impressions, as underneath the surface there are always contradictions and unexpected realities which complicate matters and force us to reconsider our initial impressions.