Mary is just as snobby as her sister Elizabeth and her father Sir Walter, but she has fewer opportunities to show her snobbery in public. While Sir Walter has people around him who quite understand what it means to be connected to the Dalrymples, Mary is a lone voice of elitism among the Musgroves. When she insists on taking precedence over Mrs. Musgrove (custom dictates that the most important people get to enter a room first, and Mary, as the daughter of a baronet, outranks her mother-in-law) or puts down the Hayters, the Musgroves don’t really feel insulted – instead, they see Mary as pushy and overly proud.
Mary sees herself as extra-special because of her father’s rank, and thinks she should be treated like the special snowflake she believes she is. So, when the others treat her like everyone else, she feels like they’re treating her worse than she deserves. The only one who can distract her out of her oversensitivity is Anne, suggesting that Anne can be just as persuasive as Lady Russell when she puts her mind to it.