bark up the wrong tree

verb

Etymology: An allusion to a situation in which a hunting dog misidentifies the tree up which it has chased an animal and positions itself at the base of another tree, barking upward at the branches.

1. To take the wrong approach to a situation; to follow a false lead; to attempt to solve a problem using mistaken assumptions about its true nature.

   “The investigator spent days trying to prove the butler committed the murder, but it turns out he was barking up the wrong tree.”

   “You're not the first man who has made such a mistake, and found he was barking up the wrong tree.”