Lady Catherine is being rather rude and bossy in questioning Elizabeth so closely about her sisters and their education and place in society. It’s more of an interrogation than polite conversation, but Elizabeth is more than equal to the task of cleverly skirting around giving a direct answer to her ladyship.
The build-up to Lady Catherine asking Elizabeth’s age is when it is established that all five Bennet sisters are ‘out’ in society at the same time. While in London society and higher aristocratic circles of wealth where girls would be given extensive educations and brought out into society with a great deal of fanfare, the Bennets have just gotten on with their social lives in Hertfordshire without much abiding by the fussier rules of high society.
Lady Catherine’s astonishment that the Bennet girls had no governess and are not being Properly Brought Out is likely a kind of passive-aggressive comment on the family’s lack of standing and money. Elizabeth resists this put-down by pointing out that they’re all doing Just Fine, Thanks; and while perhaps Lydia, the youngest sister, is a little young to be out in society at just the age of fifteen (many girls only being presented at Court from the age of seventeen,) it is not unheard of for young ladies of that age to attend parties and dances, particularly in the country where genteel company may be more scarce and the etiquette of social obligations more relaxed to just allow people to have a good time.
Lady Catherine needs to wrest back control of the conversation, however, so she immediately and directly asks Elizabeth’s age, which would likely lead to more passive-aggressive reflections upon how long she has had to make a good match, and why she has not yet made one yet, and how long she may have left, and whether she is holding back her younger sisters’ chances by failing to get married quickly…this is all unsaid, of course, but these are the conventions of the time and class they are all a part of, and nobody could be unaware of the doorway Lady Catherine is opening by the force and direction of her questioning.
Elizabeth’s dodge of “well, since my three YOUNGER sisters are QUITE GROWN-UP ENOUGH to be out in the ALMIGHTY GOOD SOCIETY like FULLY ADULT WOMEN then I must be SOOOO OOOOOLD I really can’t even BEGIN to tell you how ANCIENT I am Lady Catherine you would SWOON to hear how DECREPIT A SPINSTER I AM” is a master-class in being polite but petty. It quite puts Lady Catherine on the back-foot and forces her to admit that she could have quite easily and correctly guessed Eliza’s age for herself (“You cannot be more than twenty, I am sure, therefore you need not conceal your age.”) So her ladyship is made to own that she had no real reason to be so forward with Miss Elizabeth apart from her own prying manners, and Lizzy’s response is so mildly sarcastic as it plays into stereotypes of spinsters ashamed of their ages that nobody can even call her out on it for being a tart-tongued little saucepot, rather Lady Catherine must console her like “oh no, come on, we all know you’re still plenty young, geez…” but in doing so must tacitly acknowledge her own ridiculousness in asking such questions in the first place.
All that’s left is for Elizabeth to neatly confirm her exact age; and, yes, Lady Catherine is quite right, she’s only twenty years old, so one wonders why her ladyship felt the need to even ask at all…
except if she was trying to be a bitch.It’s a conversational power-move such as Lady Catherine does not often encounter among those who are socially-inferior to her.