Due to some popular TV trainers, the idea of dominance has taken on a major role in contemporary dog training conversations. The term has its origins in the 1940s, when it was used to describe the interactions of captive wolves. Some wolves seemed to rank higher in the captive pack than others, taking food first, mating preferentially, and leading the others. Some dog trainers decided to apply this philosophy to dogs, ascribing behavioral problems to the fact that the dog didn't see humans as "alphas" or "dominant" enough.
Is the dog on your bed and refusing to get off? That's because he's dominant and thinks he owns the space. Is your dog pulling you down the street on the leash? That's because he's dominant and thinks you are his follower. Does he growl when you come near his food bowl? That's because he's dominant and doesn't respect your right to bother him while he's eating.
This philosophy often leads people to take the next step and to establish so-called dominance by taking physical action with the dog. The most common and problematic step is to engage in something called "alpha rolling" the dog. This move is intended to imitate something wild wolves supposedly do. The "alpha" wolf, in order to show he's leader, pins the other wolf to the ground by his throat. So the human, having arrived at the conclusion that his dog doesn't respect him enough, punishes him for bad behavior by pinning him to the ground by the throat. It sounds like it could work, and most of us would interpret this technique in a relatively gentle way and do it without hurting or surprising the dog too much. However, the alpha roll and other techniques like it are unequivocally a bad idea. There is never a situation in which pinning your dog to the ground by his throat is part of effective training.
Why not? First, let's address the reality of wild wolves and debunk the myth of dominance at its roots. It turns out that wolf packs in the wild do not typically engage in the physical conflicts that were observed in captive wolves. When wild wolves fight, they don't do so to establish rank; rather, they fight to the point of injury or death. In reality, nearly all pack-level interactions are all about avoiding a physical conflict by using body language and vocalization.
Don't believe me? Check out what L. David Mech, one of the originators of dominance theory, has to say about it these days. Actually, he substantially revised his wolf theories about fifteen years ago, but many dog trainers have not caught up, despite the fact that the Association of Pet Dog Trainers, the largest, most reputable professional organization for pet dog trainers, has made a very clear position statement on the subject of training dogs through the lens of dominance.
Good leadership in modern, science-based dog training is all about clarity and setting your dog up to succeed. It's not about ascribing undesired behaviors to pseudo-scientific hokum about alpha dogs and then intimidating the dog through physical coercion or pain.
"But," you say, "I've seen that guy do it on TV and then the dog stops with the bad behavior. If it's such a bad idea, why does it seem to work?" It seems to work sometimes because when you intimidate a dog that badly, one of the possible reactions is that the dog will become very still in an attempt to show he's not a threat. Rather than fighting and provoking more aggression from you, the dog decides to freeze in the hope you'll leave him alone. If your puppy nips you, and you flip him onto his back and hold him by the throat, there's a good chance he'll freeze, especially if you do it roughly. However, what you're now holding to the ground is a puppy who is terrified that you'll actually hurt him. You are not a leader; you are a bully.
Even assuming for a moment that dogs see humans as other dogs, if you went to another pack member, grabbed him by the neck, and threw him to the ground, he could, quite reasonably, assume that you were trying to murder him, and he would react accordingly. On TV, sometimes that means the dog freezes, and sometimes that means the human gets bitten rather badly. The nastiest bites are typically given by dogs who are in fear for their lives. When you pin your dog, you're asking for stitches, not obedience.
This kind of leadership philosophy creates no end of headaches for us who have to train real-world dogs with no TV cameras pointed at us. Owners come in with dogs who are alternately terrorized and energized by their owners. When you intimidate a dog who's jumping or biting, you often see the jumping or biting stop—only for as long as the dog is actually afraid. It's long enough for a TV camera to document what looks like success (though sometimes the cameras document a nasty bite instead), but if you actually have to live with the dog, what you typically end up seeing is a dog who ends up being highly energized and confused a few minutes or hours later. The dog's trust in people gets broken down, and the handler has provided little clarity for he what he actually wants.
Looking at dogs through the lens of dominance is a recipe for broken trust in many cases, and in some cases, it teaches dogs to bite humans as a last resort to fight back against what they may perceive as a physical threat. If your understanding of dominance leads you to poke, hit, kick, yell at, or pin your dog, it's leading you in exactly the wrong direction. You may get the short term appearance of calmness or a short-lived reduction in the bad behavior, but helplessness isn't the kind of calmness you want. You may teach your dog that doing that undesired thing leads you to become physical and intimidating, but is that really what you want motivating your dog's obedience? You can sometimes teach a dog not to jump by kneeing him in the chest, but is that really the kind of trainer you want to be?
Dogs really can be obnoxious sometimes. They can jump all over you, steal food, pull on the leash, and do a dozen other things that are incompatible with a happy human-dog relationship. However, they don't do these things because they think they are the lead wolf in a mixed pack of dogs and humans, and viewing their undesired behavior through the lens of dominance is a recipe for broken trust and, in some cases, a nasty bite.
So no, your dog's not dominant. Wild wolves don't establish dominance hierarchies in the first place; in the second, dogs aren't identical to wolves anyway; and lastly, your dog doesn't really see you as another dog. If your dog is doing something undesirable, that means he's not trained for that situation. It's your job to teach him, not to threaten him, and there are a lot of ways to change your dog's behavior without relying on intimidation or discomfort as your go-to response.