Eat humble pie
Act submissively and apologetically, especially in admitting an error.
In the USA, since the mid 19th century, anyone who had occasion to 'eat his words' by humiliatingly recanting something would be said to 'eat crow' (previously 'eat boiled crow'). In the UK we 'eat humble pie'. The unpalatability of crow, boiled or otherwise, seems clear, but what about humble pie?
In the 14th century, the numbles (or noumbles, nomblys, noubles) was the name given to the heart, liver, entrails etc. of animals, especially of deer - what we now call offal or lights. By the 15th century this had migrated to umbles, although the words co-existed for some time. There are many references to both words in Old English and Middle English texts from 1330 onward. Umbles were used as an ingredient in pies, although the first record of 'umble pie' in print is as late as the 17th century. Samuel Pepys makes many references to such pies in his diary; for example, on 5th July 1662:
"I having some venison given me a day or two ago, and so I had a shoulder roasted, another baked, and the umbles baked in a pie, and all very well done."
and on 8th July 1663:
"Mrs Turner came in and did bring us an Umble-pie hot out of her oven, extraordinarily good."
It is possible that it was the pies that caused the move from numbles to umbles. 'A numble pie' could easily have become an umble pie', in the same way that 'a napron' became 'an apron' and 'an ewt' became 'a newt'. This changing of the boundaries between words is called metanalysis and is commonplace in English.
The adjective humble, meaning 'of lowly rank' or 'having a low estimate of oneself' derived separately from umbles, which derives from Latin and Old French words for loins. (Incidentally, if you feel like girding your loins and aren't sure exactly where they are, the OED coyly describes them as 'the parts of the body that should covered with clothing'). The similarity of the sound of the words, and the fact that umble pie was often eaten by those of humble situation could easily have been the reason for 'eat humble pie' to have come to have its current idiomatic meaning.