The story
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.
Etymology from Wiktionary, CC BY-SA 4.0.
bark up the wrong tree
Today it means: 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. Full definition →