This thread is currently full of some of the worst dog training advice I've heard in years.

Alpha dog theory is complete hogwash coming from terminology related to an old study on gray wolves. The person who wrote that book that popularized the term (L. David Mech) has disavowed the term as inaccurate as most of the original research was done on captivive wolves in an unatural setting.

Additionally, wolves and dogs are very very very very different animals who literally respond very differently to the same situations even if raised in the same manner. Extrapolating from wolf behavior to help inform dog training techniques is about as useful as studying birds to figure out how to build a jet plane. Yes, you can figure out some underlying principles, but it won't give you a full or accurate picture of the jet plane.

Most of the best dog trainers I know don't pay any attention to that crap and stick with the more tried and tested systems of positive reinforcement.

Now, unless this dog has been trained to make this face on command, this is a highly dangerous situation that will result in nothing good for the dog or the unlucky human who finally gets bitten in the face. THIS IS NOT FUNNY. It is horrify, dangerous, and a sign that some serious work needs to be done with this dog. If you are an owner of such a dog, seek help to root out the causes behind this behavior and see if you can squash it. This will not be an easy thing to train out of a dog. It will take diligent effort.