Get the Wrong End of the Stick

Origin

Picture a long, simple stick, perhaps used for stirring something unpleasant or for prodding. One end is clean and safe to handle, while the other is dirty, sticky, or even sharp. To 'get the wrong end of the stick' literally meant to grasp the unsavory or dangerous end, making the task difficult or unpleasant. This vivid, physical image of an awkward or painful misstep quickly became a metaphor in the English language. By the early 20th century, it had firmly established itself as a common idiom to describe a complete misunderstanding, where one has completely misinterpreted a situation or statement, much like holding a tool by its least advantageous part.