I have never understood that either. There are times when men need to put the seat down and they just... put the seat down.
Likewise, as the writer implies, the best presentation of a toilet is with the cover down, which makes it gender-neutral. Both men AND women must adjust the toilet to their respective needs.
Personally I just put in a bidet and use it as a urinal...solved the whole toilet see thing because its doesn’t have one..and women can’t complaint because bidets are classy European stuff don’t you know