"It is disturbing because it makes a number of assumptions, which seem skewed from reality."

The underlying biological reality is that making children is more costly for women than for men. The rest follows from that.

I think therefore that you have the skewed view.

"I don't think the transactional and combative assumption of gender relations is really applicable"

It is the low level consideration of evolution - other things are layered on top, like the construct of "love" enabling people to stick together.

"the man is "convincing" the woman to have "their" child, and shouldn't "get it for free""

So you don't think a man fathering a child should take care of the mother and child? You wouldn't think it bad style to father a child and then leave mother and child to their own devices?

In any case, as I explained, the mother invests more into bringing the child to life than the father, so doesn't it seem fair if the father tries to even the scales by providing other things?

"In my reality, women usually want to have children, even more so than men."

Sure, but they need food and shelter to succeed in raising those children.