A sign of mental illness is having delusion, for example thinking you are Napoleon. A man who thinks he is really a woman despite physical evidence to the contrary is suffering from a mental illness.
I'd say some great places to start might be:
- Understanding Gender: https://www.genderspectrum.org/quick-links/understanding-gen...
- Gender Revolution (Netflix documentary w/ Katie Couric): https://www.netflix.com/title/80186731