To get the wrong end of the stick

勘違いしてしまう、という意味です。例えばこんな状況に使えます。

A: “I think Mark is cheating on his wife! I saw him hugging a strange woman today!”
B: “I think you may have gotten the wrong end of the stick. It must be his sister. She’s back in town for a couple of days.”

「反対側の棒を掴む=間違えて捉えてしまう」ということですね!勘違いしてしまった時に是非言ってみましょう!