"When you have made a serious error and need to acknowledge it humbly, it is highly probable that the expression you use to describe the process has something to do with food.
The best-known traditional expression of this type in the US is to eat crow. The origin seems fairly obvious: the meat of the crow, being a carnivore, is presumably rank and extremely distasteful, and the experience is easily equated to the mental anguish of being forced to admit one’s fallibility. But you may understand that my desire for accuracy has not led me so far as trying the experiment for myself, though taking a line through rook pie, which I tried once at an over-enthusiastic historical reconstruction, it seems a reasonable assumption. We need someone like the eccentric Victorian surgeon Frank Buckland, founder of the London Acclimatisation Society—dedicated to introducing useful new plants and animals into countries where they were unknown—whose hobby was eating his way through the animal kingdom, trying out delicacies such as roast giraffe and elephant trunk soup. He once returned from holiday to find that a leopard at the London Zoo had died and been interred in a flower bed; seizing a spade, he immediately dug it up to try it. He is on record as remarking that “the very worst thing he ever ate was a mole”, but I can’t find out what he thought of crows. Volunteers to make empirical observations should form an orderly queue.
An article published in the Atlanta Constitution in 1888 claims that, towards the end of the war of 1812, an American went hunting and by accident crossed behind the British lines, where he shot a crow. He was caught by a British officer, who, complimenting him on his fine shooting, persuaded him to hand over his gun. This officer then levelled his gun and said that as a punishment the American must take a bite of the crow. The American obeyed, but when the British officer returned his gun he took his revenge by making him eat the rest of the bird. This is such an inventive novelisation of the phrase’s etymology that it seems a shame to point out that the original expression is not recorded until the 1850s, and that its original form was to eat boiled crow, whereas the story makes no mention of boiling the bird."
http://www.worldwidewords.org/articles/eatcrow.htm