Wikipedia explains it this way: Eating crow (archaically, eating boiled crow) is an English-language idiom meaning humiliation by admitting wrongness or having been proven wrong after taking a strong position. Eating crow is presumably foul-tasting in the same way that being proven wrong might be emotionally hard to swallow. Eating crow is of a family of idioms having to do with eating and being proven incorrect, such as to "eat dirt", to "eat your words", and to "eat your hat" (or shoe).
Saturday we discovered a new (to us) shop. The Crows Corner in Edgerton, OH was a delight--I'm standing outside it at this link. It's family-owned and many of the items are rustic crafts made by the owners and their young daughters. I purchased this crow (Shhhhhhh! Mostly for the pattern for my "wonder working" husband--who by the way is making progress on the doll house!). I'm still trying to figure out why I am attracted to crows. Maybe it's their black "attire". I like to wear black and feel most elegant when I'm wearing a black dress.
While I like their color and profile, I do NOT enjoy "eating crow"!