Knowyourphrase.com explains that this expression means to “…make a wrong assumption about someone or something.” A person being wrongly accused might use the phrase to tell the accuser they are wrong. The origin is said to be from the use of hunting dogs to trail prey. The dogs give chase; the prey crawls up a tree and perhaps jumps to a nearby tree. Therefore, the dog is “…barking up the wrong tree.” The expression was used in the early 19^th century when the Knickerbocker Magazine in 1836 had a statement that read, “’You’ve been barking up the wrong tree, cried the Ohioan.”