What is the meaning of this metaphor?
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The narrator believes life is difficult for both genders, and that it requires self-confidence. Self-confidence is often attained, she believes, by considering other people inferior in relation to oneself. She says that throughout history, women have served as models of inferiority who enlarge the superiority of men: "looking-glasses possessing the magic and delicious power of reflecting the figure of man at twice its natural size." Men logically become angry and defensive if women ever criticize them, then, since women cease to be inferior and the men accordingly lose the status of superiority on which they are dependent.
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Men, used to feeling superior at the expense of women, grow angry and fearful when their superiority is threatened. Hence, they cut down the women in an attempt to enlarge themselves, as the narrator describes in the "looking-glass" metaphor.