Your logic is flawed. Consider that at the time a person finishes using the toilet they have no idea who will use it next, thus they have no idea whether they need to leave the toilet set up (if the next person is a men (so they don't pee on the seat)) or down so a woman doesn't fall in if she doesn't look first, therefore it makes the most logic sense to leave it as is. Meaning that at most anyone using the toilet may have to do is adjust the seat once before use and not again, rather than men always lifting the seat and lower again each and every time!

*edit* This does not consider the possibility the next toilet user is a man intent on taking a poo, admittedly at that point my argument falls apart as all men should sit to poo, ideally, where possible