wrong end of the stick, the
A misunderstanding or distortion, as in We ordered a “full quart” of rice, but the clerk got hold of the wrong end of the stick and sent us “four quarts” instead. This expression refers to a walking stick held upside down, which does not help a walker much. It originated in the 1400s as worse end of the staff and changed to the current wording only in the late 1800s. Also see short end of the stick.