Men and women should be equal. That doesn't mean they are the same. They should have the same access to economic, professional, and political power. But again, that doesn't mean they are the same. It is difficult to accept differences when we can see only through our own eyes.
It's very easy to have a relationship in which one party dominates the other. Sharing power equitably, however, is a challenge.
Of course men and women should be equal in society. That does not mean they are or that they have always been.
For this topic you really have to consider so many factors: women in the US have equal rights under the law, but that doesn't mean that every woman in America has equality. Laws are a great start but they can't change attitudes.
As for your references to God: I think you need to consider the difference between religious dogma and the rules of religion made by man, and what God "says". Each of us believes different things about our creator. The reason religion can be so divisive is that there is no proof either way. Scriptures and other religious writings, were written by the hand of a man. Whether you believe that there was divine intervention or not is a matter of personal belief. No one can say that God says women are inferior. You can believe that, but you have no proof.
Additionally we have to consider social constructs and how they have changed and continue to change over time. Matriarchal societies are not nonexistant and often in male dominated societies woman find alternative ways of exerting power. Women in China had no political power for centuries but their writings and art, and their influence within the home has had huge affects on Chinese Society. Look at the salons in Europe during the Renaissance and Enlightenment period. Women almost always ran these and the most prominent political, scientific, artistic and other ideas of the time grew in the parlors of these women, most of whom were still politically disenfranchised. In modern America the increase in single parent households means that there are whole families and kin units and communities being run by mothers and grandmothers and aunts.
Of course men should not rule over women. Men and women should be partners. There is a certain amount of equality that should occur, but most of it is give and take. You have to learn to accept the strengths of each gender and let the genders work together on equal terms.
This is something of a straw man in any Western country at least. The idea that men rule over women at all is pretty much out of date. Hardly anyone would argue today that men deserve to rule over women in the way you suggest. Perhaps this would have been more of a subject of controversy 40 years ago, but today there are very few people who would seriously take the position that men should dominate women.
Surely the argument could be made without characterizing men as "ape-like." I agree with your basic point, however. Clearly gender equality is an essential part of a modern society. While there are still many vestiges of a patriarchal past, I do think women's equality is closer at hand than ever before. But there are still barriers to be overcome, and the number of people who hold very "traditional" views about gender roles may be surprising to some.