Not only is that totally out of the context and nuance of Deut. 22 and its sexual and homosexual prohibitions, it's silly to think the reverse...ie cross dressing men were trying to gain privilege restricted only to women.
When women were property back then and restricted to the most menial of liberties, your logic falls on its face.
Ignore what you want, pick and choose what to believe...ignorance is bliss I suppose.
Dueteronomy 22 does not concern itself with sexual prohibitions - it is about dealing fairly with others. If you appreciate context, then you must admit my argument is strengthened by consideration thereof.