Bone to pick with someone
(PW) complaint, argument
I heard that you have rejected my proposal. I’m upset and have a bone to pick with you.
(MW) bone to pick : a matter to argue or complain about
(thePhraseFinder)
"Bone to pick," dates back to the 16th century, simply refers to a dog chewing endlessly on, and "picking clean," a large bone. A "bone to pick" is thus a subject or issue that is expected to require considerable discussion or argument. A similar phrase, "bone of contention," meaning an issue over which two people argue, also dates back to the 1500s and refers, appropriately, to two dogs fighting over an especially choice bone.
: : http://www.word-detective.com/052301.html
: It has a slightly different meaning here in Ireland. 'I have a bone to pick with you' means 'I believe you have done me wrong and I want to know why.'
:::Here in the States the meaning is the same. A 'bone to pick' is an issue to be discussed and resolved between individuals.
(freedictionary)
bone of contention
The subject of a dispute.
bone to pick
Grounds for a complaint or dispute.
(usingEnglish) I've got a bone to pick with you
If somebody says this, they mean that they have some complaint to make against the person they are addressing.