First off, we should first understand the definition of "Dominance."
Dominance is defined as a relationship between individual animals that is established by force/aggression and submission, to determine who has priority access to multiple resources such as food, preferred resting spots, and mates (Bernstein 1981; Drews 1993).
How did the dominance model become? It came about from misinterpreted wolf studies. Wolf packs are made up of a father, mother and their children. Leading wolf researchers today are not calling the mother and father "Alpha" anymore! They call them "breeding" male and female because all their entitled to do is BREED! The mother and father don't necessarily eat first. Actually, if one of their children is on a kill first they'll back off if the younger wolf shows teeth. The father and mother don't force their children on their sides. The children roll over for them on their own free will. The father and mother don't claim things and definitely don't take resources from their children. Check out what David L. Mech(leading wolf researcher who coined the phrase "Alpha", who now calls them breeding male or female) says about the term "Alpha."
It's silly really to treat a domestic dog like they're trying to take over the house, because their not! And it's even sillier to compare them to wolves. The domestic dog did evolve from the wolf but that was over 15,000 years ago. Because of human involvement in selecting dogs to breed, the only appropriate model to compare the domestic dog is the domestic dog.
If your dog eats first or wins the game of tug of war will he try taking over the house? No, that mentality of thinking is SO 20 years ago! Dog training and dog behavior has made such advances that leading behaviorists and trainers have debunked dominance theory. Following this model just makes you a bully in the dog's eyes and proves that trainers following this model don't bother continuing their education. Check out The American Veterinarian Society of Animal Behavior's position on "dominance theory."
So why do some trainers still follow this model? I would assume they don't read or continue their education.