Not having a period would be rather stupid reason, as for males it not even possible. Second, that does not explain why little girls would have the right to wear feminine cloths before they get their first periods. Both the guys and the girls have their own issues and problems throughout their life. And if the periods would be the reason for the girls to have the right to wear girl's clothes than for girls would have to have had and erection with the male ejaculation(just an example, I don't care what clothes people wear as long as they like the clothes themselves) to have the right to wear guy's cloths, which also is not possible.
The second option you mention could be possible, but that would make the male in the dress most likely a homosexual, which would be another story together. Hiding ones sexuality inside a relationship is not a good thing. In this case one would just have to make it clear that one is not gay of any kind. Nothing would change in the relationship between them, which is hard to explain but it has to be done.