Estrogen production is supposed to be intricately entwined with pregnancy or so an article somewhere said.
It probably regulates and directs the body towards bringing conception to term. Stuff like mood swings, morning sickness, yearnings, fuller breasts and milk production probably get triggered by having a high enough level of estrogen screwing you from the inside.
I say probably because I don't know it's true.

Obviously big and strong

Probably because the argument completely ignores social dynamics.

I think the answer to most of your hypotheticals there is, probably yes, based on what I'm remembering. I think the working theory was that sexism comes about as a result of the idea of ownership through agriculture, i.e. land ownership, labor animals, stuff like that. Men lock down women because ensuring female chastity is a way for men to make sure that their heirs are the ones that are doing the heiring, that their kids are the ones that are going to get the inheritance, rather than anyone else.

The idea is that in parts of the world where land ownership, agriculture, labor animals, aren't as common, there's generally less sexism, and even some amount of matriarchy, since women can kind of have more power over men through the fact that they're the ones who can give birth. There's definitely an amount of "grug bigger than grugalina, grug hit grugalina with stick unless grug gets head", or whatever, and that probably happened in ancient times, but it's also a more complicated story than that. This article was a pretty good read on the whole deal, if you're interested in more of that theory.

If you reversed the dynamic, here, it would kind of depend on the mechanism, I would think. Like, are women now the "stronger" sex, or do men still have like, higher levels of bone density, higher predisposition to hypertrophy, and probably more importantly, are men still socialized to like, be basically completely insane, and more kind of hyper-specialized? Or are we just doing what's basically an entire swap of the sexual dynamics and biology? If it's the former, I think, you know, probably no shit, that everything's basically the same, but "swapped". If it's the latter, though, and there's some amount of change in the actual power dynamic, or some amount of relative change in the biology, I'd expect that to have maybe more interesting results.

This is the type of shit I'm always kind of frustrated that shows like star trek don't tackle, cause there's a lot of different and cool places you could go with something lack that, in terms of character concepts, societies, alien races. What about lizard people that lay eggs? Would they have kind of a more egalitarian society, or would they have other problems? What about people who reproduced by budding? What about, you know, as said formerly, if the women were the stronger sex, but were also the ones who got pregnant, as it is with many animals? I dunno, it's kind of interesting, you could spin a lot out of it.

I think it would be something like the Spotted Hyenas. Where one sex very dominant.

probably the autism