In practice though, it's not about those types of situations as much as it's about how we are subtly conditioned to accept disparity. As I said, it happens in the work place when women are held to different behavioral standards. It happens in advertising (Target photoshopping a gap between a ten year old's legs for swimsuits). It happens when guys want to fool around with girls who put out but marry the chaste girl.
Now of course men and women are different, but are you honestly going to argue there aren't vestiges of a mostly patriarchal history that affect society today by creating unnatural societal pressures on women? As you yourself pointed out, valuing chasteness in women is one such vestige of patriarchy, and it is reflected subtly in society to this day.
This is an experiment that I personally haven't done in a few years, but was pretty reliable whenever I tried it. Take a random men's magazine and a random women's magazine off the periodical shelves. Compare the love/sex related articles and headlines. Usually women's magazines are about getting "the" guy, figuring out if he's "the one," etc. There's a slant towards content being about long term relationships and finding/keeping one man. Even sex advice is usually presented such that the context is pleasing one guy and hanging onto him. Comparatively, men's magazines are about getting girls. It's about pick-up moves to get more dates, it's about sex moves that will please more women.
It's not that the people who write this content are sexist. But they write what sells. They are catering to the implicit assumptions of society that exert force on what their readers are trying to do. That men play the field, and women should look to settle down and have to work on making themselves that girl the guy settles for.
In the long term, one hopes that just as much as we accept whatever natural differences there are between the sexes, we don't limit individuals based on expectations of their sex. We don't ostracize people for not adhering to gender norms. As I said earlier, the point of gender equality movements isn't to create equal outcome, it's to the create equal opportunity. For example in STEM, it's not about getting 50/50 splits in those fields, it's about the final split being reflective of whatever the natural split is. (And I'm not bringing that example up to open a debate, just to illustrate how the theoretical goal looks in effect.)
And again, gender norms work against men too. As we've briefly discussed earlier, boys who don't fit the typical masculine standards are made to feel bad, including by women who are influenced subconsciously by how they are told men are supposed to be. Or as you said, men are stuck paying child support for kids who aren't theirs because our system was founded on the idea of men as the provider and mothers who can't fend for their own children.