This delightful saying is a mash up of “give credit where credit is due”, “give the devil his due”, and “every dog has its day”. Perhaps there is a homonym mix up here as well, as in “dog doo”? Who knows what lurks in the subconscious mind? A shout out to Bill B. who heard this one from Dr. Marty Kraus.
I think this is a mash up of “tail wagging the dog” (a situation where a small part is controlling the whole of something) and “his bark is worse than his bite” (person seems more hostile than he really is). The latter includes the visual of a dog biting and hence the confusion. I say think because there are other possible explanations for the mix up. My “ol pal” thinks the phrase “man bites dog” (aphorism in journalism which describes how an unusual, infrequent event is more likely to be reported as news than an ordinary, everyday occurrence) is involved since it evokes a visual of both parties biting. There is also the phrase “don’t bite the hand that feeds you” (don’t treat someone badly who is helping you). I guess this is an unsolved “case”. Any other suggestions?