From Longman Dictionary of Contemporary Englishget the wrong end of the stickget the wrong end of the stickBritish English informalUNDERSTAND to understand a situation in completely the wrong way Geoff had got the wrong end of the stick, and thought I was angry with him. → wrong
Examples from the Corpus
get the wrong end of the stick• Maybe I got the wrong end of the stick. I thought she was leaving him, not the other way round. 