wrong end of the stick, the

the wrong end of the stick

A misunderstanding, miscommunication, or distortion of the facts. He must have gotten hold of the wrong end of the stick about something when I was talking to him earlier, because he has started acting really odd whenever I see him now. The senator found herself at the wrong end of the stick after mistakenly saying during an interview that she would like to see funding for public education cut in half.
See also: end, of, stick, wrong
Farlex Dictionary of Idioms.

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.
See also: end, of, wrong
The American Heritage® Dictionary of Idioms by Christine Ammer.
See also:
  • the wrong end of the stick
  • wrong end of the stick, (got hold of) the
  • get (one's) lines crossed
  • get your lines/wires crossed
  • get (one's) signals crossed
  • get (the) clearance to have (something)
  • have a head start
  • build a fire under (someone or something)
  • bomb out on (something)
  • get plugged into (something)