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Eating crow is a colloquial idiom, used in some English-speaking countries, that means humiliation by admitting having been proven wrong after taking a strong position. The crow is a carrion-eater that is presumably repulsive to eat in the same way that being proven wrong might be emotionally hard to swallow. The exact origin of the idiom is unknown, but it probably began with an American story published around 1850 about a dim-witted New York farmer.
Eating crow is of a family of idioms having to do with eating and being proven incorrect, such as to "eat dirt" and to "eat your hat" (or shoe), all probably originating from "to eat one's words", which first appears in print in 1571 in one of John Calvin's tracts, on Psalm 62: "God eateth not his words when he hath once spoken".
An Australian demonym for South Australian people is croweater but it does not carry the same idiomatic meaning as eating crow.