My understanding of a relationship like this is that the man of the house is ultimately responsible for making the decisions for what is best for the family. When he is considered the provider and the protector, he brings to the home what he feels is best, and he protects the family from whatever outside environmental factors he feels is detrimental to the family. Within that realm, however, it is argued that a woman has the freedom to choose how to apply the decisions that man makes.
Under these conditions, a woman may not have as many freedoms as a man and is subject to his decisions, but it is argued that she is not as vulnerable to the outside harsh world as a man is, and therefore in a way seen as privileged with those protections in place.
Those who advocate these "complimentarian" gender roles typically support their stance with these arguments. They will also introduce biological functions as further evidence for gender roles (a woman lactates, a man has testosterone, etc.).
My experience has shown me there are a number of women and men who are happy to feel as if all their problems are overseen, and they can just let somebody else make the decisions. What I think the traditional gender roles do is tell only half the story, and assume that males overall do not want to fulfill a submissive role in a power-distinct relationship, or that females are not suited to a leadership role, or that males will not be happy if females dominate or become assertive.
I have not found that to be the case across the board. There are too many variables with personality types, religious beliefs and non-beliefs, and cultural dynamics to assume a one-size-fits-all formula for gender in relationships.
