noun
having the right to say; being in a position to criticize
Fixed expression used almost exclusively in negative or rhetorical contexts to mean someone is not in a position to say something, often because they are guilty of the same thing. Common patterns: 言えた義理ではない, 言えた義理か, 言えた義理じゃない.
お前にだけは言えた義理じゃないけど、もう少し早く来てほしかった。
I know I'm not really in a position to say this to you, but I wish you had come a little earlier.
自分が遅刻したくせに、人に時間を守れなんて言えた義理か。
You were late yourself, so you have no right to tell others to be punctual.
The phrase combines the potential form of 言う (to say) with 義理 (duty, rightness), literally 'a duty one can say'. The exact origin is uncertain, but it functions as a fixed expression for questioning someone's right to speak.