Men have always been the dominant sex because we are stronger emotionally and physically. This can be either a virtue when it is used wisely, or a vice when it is abused. In an ordered society, men will use their dominant position to protect women. It is the responsibility that comes along with being put in the dominant position. It is the same as in the army - the officer has been put in a position of power over his soldiers. As a result, his responsibility is to ensure the safety of his soldiers, and put their welfare above his own at all times. Likewise, when a man opens a door for a woman, he is saying "I am stronger than you, but I will use my power to serve you." That is the historical/traditional basis for why men open doors for women, and why women don't open doors for men. It is the same reason why women and children were traditionally evacuated from a sinking vessel first - the strong protect the vulnerable.
I acknowledge of course that feminism refuses to admit the reality that men are stronger than women, and that's the self-defeating aspect of it. If men offer to put women first, feminism discourages women from accepting the offer, calling it patronising. So men have become less inclined to put women first, yet (try as feminists might to change the natural order) men remain in the stronger position. And then feminists wonder why so many men end up becoming abusive bastards.