Mrs. Steerfoth behaves abominably towards David and Mr. Peggotty when they go to see her in Highgate. They've come to tell her that her son has run off with Emily. In those days, such an elopement would've been a serious scandal, and Mr. Peggoty wants to do everything he can to protect his niece's reputation. He's worried that she might end up being seduced and abandoned. And for a young woman in that position, that would mean social disgrace. Not unreasonably, then, and in accordance with the standard practice of the time, Mr. Peggotty asks Mrs. Steerforth to give her blessing to her son's marrying Emily, as way of making an honest woman of her.
But Mrs. Steerforth flatly refuses. As well being an over-indulgent mother to her spoiled brat of a son, she's also a crashing snob and so doesn't want any child of hers to get hitched to the daughter of a humble fisherman. When Mr. Peggotty points out that he loves his niece just as much as Mrs. Steerforth loves her son, Mrs. Steerforth scoffs at the very idea, claiming that this is impossible. Clearly this is someone who believes that those from lower down the social ladder are incapable of finer feelings. Such an outrageous remark only makes Mrs. Steerforth even more thoroughly unpleasant, and that takes some doing.