Used when someone makes an unfounded claim or starts a fight over a trivial or fabricated reason. Often appears in phrases like 言いがかりをつける (to pick a quarrel or make a false accusation).
statement one cannot take back; irrevocable remark
Refers to a statement that, once made, cannot be retracted or undone. Less common than sense 1; often used in contexts where one must take responsibility for one's words.