Get the wrong end of the stick Informal

To misunderstand what someone means or what is happening, often by drawing the opposite or an incorrect conclusion from the available information. The phrase is especially common when correcting a mistaken impression.

The expression is established in British English, but its precise historical source is disputed. A familiar explanation imagines a person grasping the wrong end of a stick or tool and consequently using it incorrectly. That image makes the metaphor memorable, yet it should not be treated as a documented account of its creation. The key idea is taking hold of something from the wrong side: a small initial error leads to a mistaken interpretation of the whole situation. By the nineteenth and twentieth centuries the phrase had become an everyday way to describe misunderstandings, particularly when someone draws a false inference about another person’s motives. It does not imply dishonesty; the misunderstanding may be entirely innocent.

You’ve got the wrong end of the stick — I’m not quitting, I’m changing departments.

I think she got the wrong end of the stick about why we cancelled.

Don’t get the wrong end of the stick; I’m asking for help, not blaming you.