I disagree that it should always be the woman staying home (or always the same parent through the children’s adolescence, or that both parents should have different genders, or) but I think the premise is sound.
They’re also objectively correct that women should, on average, be having children earlier (but wrong when they want it to be before the age of majority, or when they want to lower that age, or permit child marriage, or want to deny that couple sound sex education and medical care.)