Get the wrong end of the stick

To misunderstand a situation or what someone has said.

Examples

I think you've got the wrong end of the stick – I wasn't criticising you.
He got the wrong end of the stick and turned up on Saturday instead of Sunday.

How to use it

Informal, mainly British English. Usually with "get" or "have".

bark up the wrong treeTo have the wrong idea about something or look for an answer in the wrong place.