Comparing the social hierarchy of wolves to dogs and thinking we need to “dominate” dogs according to it is an outdated belief. First of all, even the hierarchy of wolves is much more flexible, wolves are peace-loving animals and do not compete for leadership as much as people generally think. Secondly, dogs are not wolves! Dogs and wolves have different mental capacities.
Dogs show very little hierarchy or competition over leadership, and their social system that has been scientifically studied is even more flexible and subtle. Dogs do not compete over leadership with people.