The phrase “barking up the wrong tree” comes from an old hunting tradition and has roots in the 19th century. It’s a colorful way to describe someone who is pursuing the wrong course of action or making a mistaken assumption.

Back in the day, hunting dogs were essential companions during hunts. Their job was to chase animals, like raccoons, squirrels, or even big game, up into the trees so that hunters could track them. However, sometimes these excited pups, in all their enthusiasm, would get a bit confused. They might run up to a tree, start barking furiously, and completely miss that their prey had scampered off to another tree altogether. The dogs thought they had cornered their target, but in reality, they were wasting their energy on the wrong tree.

The phrase is primarily an American idiom and appears to have entered popular usage in the early 19th century. One of the earliest known printed uses of the phrase is from Davy Crockett's 1833 book "Sketches and Eccentricities of Col. David Crockett, of West Tennessee." In it, Crockett says: "I told him that he was barking up the wrong tree, that he was after somebody that was not at home."

By the mid-1800s, people were using “barking up the wrong tree” to describe someone who was totally off the mark in their beliefs or actions—like accusing the wrong person or pursuing a solution that would never work.