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A fatal weakness, a vulnerable area, as in This division, which is rarely profitable, is the company's Achilles' heel. The term alludes to the Greek legend about the heroic warrior Achilles whose mother tried to make him immortal by holding the infant by his heel and dipping him into the River Styx. Eventually he was killed by an arrow shot into his undipped heel. [c. 1800]
American Heritage Idioms
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Phrase(s): Achilles’ heel
Fig. a weak point or fault in someone or something otherwise perfect or excellent. (From the legend of Greek hero Achilles, who had only one vulnerable part of his body, his heel; as an infant his mother had held him by one heel to dip him in the River Styx to make him invulnerable.) • He was very brave, but fear of spiders was his Achilles’ heel.
McGrawhill's American Idioms And Phrasal Verbs