No it’s not arbitrary and there’s no way history could have unfolded the same way with only one thing being different, that being women oppressing men.
You seem to exist in a theoretical bubble so divorced from physical, historical and biological reality I’m frankly stunned.
The bourgeoisie and the proletariat similarly do not exist arbitrarily.
The rich gain power OVER TIME as a class because certain individuals gain advantage over others, then entrench that power and advantage (in the form of wealth) through generations within their families. They then create post hoc rationalisations for why they are more advantaged, and try to put laws and customs to define those who were historically less fortunate as “inherently less deserving” and try to limit them from gaining power or encroaching on their wealth.
Have you ever read a history book? Have you ever for example read how white Europeans came to be racist? In Ancient Rome and Egypt for example, skin colour didn’t matter, but wealth and class did. People encountering different races for the first time might naturally thing “this is strange” but that’s an in group out group psychological thing common to all humans. In a cosmopolitan metropolis like Rome, people were exposed to all sorts of races and if they were rich, they were respected.
The contemporary understanding of “racism” we have today is tied to colonialism. White Europeans (British, Belgian, Dutch, Spanish etc) sought out new lands to conquer and plunder for resources to make their empires rich. In doing so they raped and pillaged and enslaved the native people of the lands they colonised. Why? Because they could. Because they had superior weapons, and unknown diseases, and because slaves were useful to achieve the goals these colonisers wanted. Their excuse and rationalisation was that these people were inherently inferior BECAUSE they were able to be conquered and enslaved. If the native peoples had been also white, the colonusers would have still done it and found a different post hoc rationalisation for why their captives were enslaved. Just like the Ancient Romans did for their slaves. Just like the Japanese did for why they considered Chinese inferior despite similar physical appearance.
History isn’t arbitrary. It’s made of the actions of billions of individuals, and those who have differences of wealth, status or power over others tend to find their influence over history and society becomes magnified all out of proportion with each generation. So the rich get richer. The colonisers continue to plunder. And they give as their reason, not the real reason — human greed, generational luck — but “we deserve it because we are better because X reason”.
Please learn some history and get out of your postmodernist, insular bubble of materialist theory. The real world is out there. Knowing the real world doesn’t mean we have to succumb to nihilism either.