What is ironic about Mildred's statement "I understand that one" in Fahrenheit 451?

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In part two, Montag encourages Mildred to read some of the books he has stolen, to preserve their marriage and examine their superficial lives. When Montag opens a book, which reads, "That favourite subject, Myself," Mildred responds by saying, "I understand that one" (Bradbury, 33). The irony of Mildred's statement is that she does not understand herself at all. Mildred lives in denial and refuses to acknowledge that her life is unfulfilling, meaningless, and superficial. In part one, Mildred attempts to commit suicide by overdosing on sleeping pills but refuses to acknowledge that she tried to kill herself the next morning. When Montag explains to his wife that she swallowed an entire bottle of sleeping pills, Mildred simply denies that anything even happened. Unlike Montag, who analyzes his life and realizes that he must make a dramatic transformation, Mildred denies that she is unhappy and unfulfilled. Overall, Mildred's comment about understanding herself is ironic because she actually knows nothing about herself. If Mildred wished to learn about herself, she would follow her husband's advice and begin examining her life.

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I guess you can say that this is ironic, although I think you can also argue that it isn't.

If it's ironic, here's how.  What she says this about is when there is the quote in the book saying "that favorite subject, myself."  What is ironic about this is that, you can argue, Millie does not even care about herself.  She is so unaware of herself that she doesn't even realize that she almost killed herself.  All she wants to do is watch the parlour walls and she has no self-awareness.

So it's ironic for her to say that she understands being interested in herself.

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