Yes, some (many? few? I don't know) women do have that kind of expectation from a man. More to the point, there are societal norms that nurture those expectations in women and in men themselves. There's no question to my mind that this is exactly the same kind of sexism that is keeping women from having successful careers in STEM academia (and elsewhere).

Like I say in another comment, sexism harms men too.

It really is not a matter of men-vs-women, here. My understanding is that these are traditional ideas about manhood and womanhood, that were useful in the past because they helped ensure societal stability and perhaps a sensible use of limited resources. But, in today's world, especially in the Western world, where the majority of men and women don't e.g. have to work the fields or do the washing by hand, these traditional ways of seeing each other only help to restrict our options. In the end, most women and most men have loved ones in the other sex (wives, sisters, mothers, daughters, husbands, sons, brothers and fathers) and it just doesn't make sense to stick to archaic ideas that want us to be somehow adversaries. Most women want the men they love to do well in their life and vice-versa. So why not work to maximise each other's options, rather than restrict them? We can work together rather than against each other to achieve our full potential, as individuals and as family units.