Determined to become engaged to Jack (whom she thinks is named Ernest) despite her mother's wishes, Gwendolen arrives at the country estate unannounced. When she meets Cecily, she is very put-off by the young, beautiful woman living in the home of the man she hopes to marry. The two women speak to each other in tones that are very polite on the surface, though the content of their conversation is rather disparaging of the other person.
In this quote, Gwendolen is referring to her father, Lord Bracknell, of whom Cecily has no knowledge. Here, Gwendolen claims that she prefers it that way, since this means that he often remains in the home and not in the public eye. Upper-class aristocratic families such as the Bracknells were wealthy to the point that work was not a necessity, thus allowing both parents to live a life of total leisure. If the fathers did work at all, it was as a member of Parliament or through investments, finance, or real estate. The lower classes, of course, needed to work outside of the home in order to provide for their families. Thus, Gwendolen's upbringing means she is attracted to men who are "domestic," meaning that they are not worn from labor and attend to duties in the home instead. She asserts that it should be women who socialize outside of the home—a progressive moment in which Wilde challenges (although humorously and ironically) traditional Victorian gender roles using a strong female character.
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