I think this has more merit conceptually than changing sex.
The idea of feeling a different age to the one you are is widespread and well understood.
Some people are "born old" ine way they are and some are always "young". Many people feel younger than they are - and having been younger there is actually some basis for this feeling ie we know what it feels like, we are not identifying as something we have never been.
Time passes obviously but how it feels is highly subjective - our perception of how time passes changes according to how much fun we are having, whether something is a new experience or one we have done lots of times, as we age our perception changes due to a variety of factors, and there's the way that different size animals perceive time differently and while we're all human some adults are twice the size of other ones.... Then there are things like menopause > do two women who are the same age but at different "stages" of life feel different in terms of their age? Maybe? And so on and so forth...
Then there is the fact that as this guy says, some people's bodies do age slower than others - due to luck, genes and how you live > this is measurable.
So this makes a LOT more sense than feeling like you are the opposite sex, comceptually.
Obviosuly it would never fly though as so many things in society are linked to age and it would be open to massive abuse with huge consequences.
While allowing men to say they're women is deemed consquences free (in a sexist society).
Of course people weren't allowed to ID into things that matter to men >> herediatary titles (primogeniture no girls thank you very much), getting pensions earlier before they were equalised (money) and so on...