The story
A reference to complaining about finding animal bones in food; compare find no bones in (“(obsolete) to experience no hindrances or obstacles; to do something without hesitation”) and have a bone to pick.
First known use, by meaning
- from 16th c. To do, indicate, or say something clearly and without hesitation, even if it may be unpleasant.
Etymology from Wiktionary, CC BY-SA 4.0.