bark up the wrong tree. To follow a red herring, i.e., a distracting bit of evidence or scent.

Dogs will tend to “tree” their or their master's prey. They sit at the base of the tree up which they have chased their quarry and bark or bay. William Safire helpfully points out that “it's not the tree, beloved of environmentalists, that is wrong, it's the dog.” Dogs act on instinct, especially in hunting mode. However, the process of domestication often results in arrested development in one aspect of predation or another. Therefore dogs will engage in predatory acts, such as baying or barking even when there is no prey. Safire suggests that even when chasing actual prey, perhaps “the dog is deceived.” However, as a lexicographer and not a zoologist or animal psychologist, I presume that he is engaging in mere speculation about this aspect of dog behavior. I would submit that while the dog may indeed be deceived, he or she might also be “playing” or just plain wrong.