It's not my normal reading material, I have to admit. I'm not sure about it at the moment, about halfway through.
Baumeister presents it as a long-form essay argument and I don't really like the lack of labelled sources and references, though there are sources at the back. To be fair, I wasn't sure what to expect but I can't gain understanding by just reading what is most comfortable. So far he hasn't turned it into an oppositional comparison of "look how we have it worse", it looks more like he's attemping to move the perspective towards ideas of motivation, evolutionary biology and a shared causal responsibility of both nurture and nature for differences between men and women.
I think these are well-recognised arguments that have been made before and he does a decent job of pointing out that this argument is about preference rather than one gender being better than another in a value-judgement sense. He also doesn't suggest anywhere that women and men should be performing certain tasks or roles, only that there are tendencies and reasons for these tendencies. Here there are the usual suspects, such as male extremity along the bell-curve and a concept of different kinds of social interactions (on average) between men and women.
The most contentious point is probably how men and women differ in their socialisation, with women being more apt towards intimate, personal relationships that are better for fostering emotional and psychological well-being and men being more drawn towards superficial, but extensive, groupings that work better for a competition of ideas. I'm probably over-simplfying a bit, though.
But the basis is how this relationship results in the abstaction of culture, as a system, and how that exploits the extremity of men by making use of their disposability in the reproductive cycle of the species.
I think the best thing here is to just quote his statement at the start of the book:
Before we get started, lets clear up a few things. This book is not against women. It is not even particularly in favour of men. Along the way I will have various, mostly positive things to say about both genders, but those are not the main point. One core interest of the book is to examine how culture exploits men. This does not mean I am denying that culture exploits women too. Many cultures exploit women, some more than others, and sometimes cruelly.
This is not a book based on personal experience. It is certainly not a complaint. I don't regard myself as a victim, either of women or of culture. Women have been good to me, with a few minor exceptions. Culture has been good to me also, also with a few minor exceptions.
Nor is this book a pitch to gain victim status for men. The modern widespread eagerness to claim victim status for one's own group makes me ill. If you read this book and end up thinking the main point was that men instead of women should be considered victims, or even assume this status alongside women, then you have completely missed my point, and I have failed to get my message across.
I don't want to be on anybody's side.