Tbh that is the part that we just starting to cover on my course, but from previous knowledge and little bits of info from my course, I will do my best to try and explain...
So basically the idea of pack theory and dominance came from studying wolves, which makes sense, since dogs are descended from wolves. What went wrong is that the wolves were not studied in their natural environment or within their natural family.
Wild wolves were captured and placed into an enclosure with other wild wolves. These wolves were not related to each other and had no clear leader, as they did in their own family groups, so disputes broke out between them, this was seen as dominance. The researchers believed that each wolf wanted to be dominant and that is how it would work with dogs and wild wolves. They'd all want to be dominant and would gain dominance through ritualistic displays and aggression.
What we now know is that wolf packs are actually family groups, a breeding pair and their off spring. The breeding pair lead by default, the older off spring help raise the younger, so they also lead the younger pack members, but not the older ones. Kind of like a flow chart based on age and experience. The younger pack members do not try to dominate the older ones. Eventually the cubs will grow up, find a mate and begin their own and thus become 'alpha' so each surviving wolf gets a chance to be pack leader in time. There are no ritualistic shows of dominance or aggression. The elders eat first, normally, because they hunted and caught the food, although in times of illness or when food is sparse they will allow the younger pack members to eat, to ensure their survival. It's a relationship based on mutual co-operation, the same as our family is.
When left to go feral dogs don't behave in the way same as wolves do, they don't have the same rigid family groups, the male dog has very little interest in sticking around to help raise the pups, the female is on her own. They'll mate with more than one spouse, even mating with members of other social groups.
They are each out for their own but will co-operate with other dogs if it is for their own gain. They catch and eat (or scavenge normally) their own meals, one leader does not feed the pack as wolves do. A dog who might show aggression with one particular other dog, in one situation, might not show aggression to another dog in the same situation, all based on their previous experience of that dog and the value of the resource they are fighting for. They are well aware injury may lead to death, so will only risk fighting if what they have is deemed worth it and they have a good chance of winning. They prefer to diffuse tension using calming signals and submissive behaviors which are normally copied by the aggressor.
They often leave one social group to join another, rather than staying in the same group like wolves. There is never a clear leader, although some of the group may naturally lead this is changeable due to the constant comings and goings of group members, it's all very flexible.
What this means to us when we are training is that dogs are adaptable and like to gain resources via co-operation rather than aggression. They don't understand pack rules or alpha rolls or eating first etc.
Also because the pup has already imprinted upon it's mother before meeting you, it is well aware that you are not the same species and you don't have the same rules as their species do.