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This has to do with the Chinese Zodiac. It is believed that the horse is an animal that symbolizes strength, being born under this sign is supposed to be bad luck for women.
It isn't bad luck to be born in the year of the horse for a woman, but rather to be born in one of the years of the fire horse. The years 1846, 1906, 1966, 2026 are the years of the fire horse, and are supposedly bad luck not only for the women born in them, but for their families as well. Esperanza doesn't believe in this bad luck, nor does her grandmother.