The right-wing view suggests that the man must lead in a relationship/marriage. The left-wing view suggests that men and women are equal. Both views rest on the supposition that the relationship between a man and a woman is static, where both parts balance each other to make a system. This view simply is not true. Marriage/relationship is a dynamic system, where both parts dissolve into a union. We can compare this relationship to that of matter and space. Matter curves space. Space then dictates how matter moves, but it not a dictator, because its curvature is created by matter itself and changes spontaneously with the flow of matter. It's a dynamic relationship that goes back and forth, feeding into each other.
We see the same dynamic in friendship. There is no such thing as a dominant or submissive friend. Such stupid ideas thankfully don't defile friendship. Great friends don't worry about who would lead their friendship. Sometimes, one party contributes more; other times, the other party or other parties contribute more while they step back. How do they decide when to lead/contribute more and when to step back? They don't. They don't have to do that because they are synchronized. They spontaneously adapt to situations and work as a team.
Members of a great team don't stay stuck in their individual roles. They go beyond their individual roles when needed and step back to allow someone else to lead when there is an exploitable opening. They coordinate spontaneously (without any top-down authority) and, thus, instantly. In this way, a great team is not simply the sum of its members but far greater than that. In football, who goes for a goal depends on who has the best opening. Other players spontaneously become assisters. In all team sports, members are supposed to adapt to the situation at hand and do what's best for the team. Watch this link.
Relationship and marriage are also team sports. When you get married, you are not just adding a person to your life but becoming a new entity, an entity that is distinct from and far greater than the sum of you and your partner. Neither party is supposed to dictate the other but engage in a harmonious spontaneity. It's like a duet. You create harmony by going back and forth to contribute towards the song rather than your song. There is no leader in a duet, nor is there a follower. The moment you try to dominate and take control, the duet becomes disharmony or just noise.