eat crow

eat crow (to display total humility, especially when shown to be wrong) — каяться, виниться, признать свою ошибку, неправоту или поражение

Example 1:...Well, it looks like I was wrong, and I'm going to have to eat crow. (dictionary.reference.com)

Example 2: I made some big promises then I had to eat crow when I couldn't fulfill them.

Example 3: The president had to eat crow over his promise not to raise taxes.

Example 4: Have you ever had to eat crow over a comment you made in a critique? I have ... more than once.

To eat crow (or “eating crow”) is an American English expression which refers to humbling yourself by admitting that a previously (and often strongly) stated opinion was wrong or incorrect. It’s roughly equivalent to the British expression “to eat humble pie”. --> see
[eat humble pie]
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Crows have a bad reputation because they are scavengers that eat dead and decaying flesh, so 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.