I agree. A transwoman wearing men's clothing would feel like she is cross-dressing. The Bible doesn't seem to recognize the trans concept but makes a point of making trans and gay behaviours an "abomination" Some primitive cultures really needed to organize their world in a simple way. Other cultures may have had more flexibility.
I think, in many ways, the societal problem comes from not those who "pass" as their gender, but those who do not, because we cannot classify them. They make use unsure, confused, because they are amgibuous to us. As a result trans people like myself, who do not pass, fall into the Uncanny valley for some people. It's fucked up, but in some ways those who feel that way can't help it, and changing means facing up to the fear they feel.