That being said, men and women are not the same.

No they are not. Because every person is an individual, no one man is the same, no one woman is the same, what makes anyone think that a man and a woman would be the same?

Men are much much more obsessed with the way their partner looks.

Some men are. Just as some women are.

Cultures across the globe also tend to put a lot of emphasis on the ability to reproduce. This is why many women find it embarrassing if they are infertile. This is also why women are kind of commoditized, because women can't create eggs the way men make sperm.

How does this relate to gender equality? It is human nature to reproduce. Some men are also embarrassed if they find out they are infertile. It makes them feel less of a man, in the exact same way. Eggs can be harvested in the same way that sperm can, it is quite possible for women to enslave the entire male population and selectively breed with only the most choicest of male studs; it could also be reciprocated equally from the other side.

It's makes perfect sense to cover women and not men, because men are attracted to physique more.

Women covet men just as much as men covet women. They are just more skilled at veiling their emotions.

Men are also physically stronger and thus able to physically overpower women.

Not every man is physically stronger than a woman, just as not every woman is stronger than a man. It is the oppressive cultures of Judaism, Islam and Christianity that belittle women and trivialise them into some delicate breakable thing. In Celtic, Teutonic, Germanic and Norse culture women fought alongside men in battle, were revered as gods and heroes. In Asia and the Americas, Africa and the Middle-East, warrior women are detailed throughout history and legend. The only thing holding a woman back from besting a man is her own motivation. We are equal in diversity, like Yin and Yang.