Fight to be Submissive?

So last night I was watching a television show and the idea was put forth that in every relationship one person is dominant and one person is submissive. It was not postulated if who played which role could change on a regular basis depending on situation, though the idea was presented that each could fight for dominance or to be the submissive. The idea that each person would struggle to be the later struck me as slightly unusual, though it seems to be a concept I can grasp with relative ease.

I haven’t really decided my overall thought process on the idea, though I admit it is interesting if taken not from the stance that obviously any two people are not identical, but from the stance that within any relationship, one person is actively dominant or actively submissive, even if neither realizes it. My main caveat for delving deeper into thought on the theory is that I have at least one relationship where I know neither of us cares in the slightest and even from empirical evidence I see no real consistant basis for saying one of us is the dominant overall.

Though perhaps that I can only find one such relationship off the top of my head means I should think the idea through more.