Neither is "wrong" per say.
Mentally ill people have been identifying as impossible things since there have been mentally ill people.
You can identify as a supernova if you like. However it is wrong to try to use political and social pressure to force other people to go along with their delusion.
Bruce Jenner got accollades and Rachel Dolezal got fired. I guess it’s A-OK for NAACP to fire someone because their skin is white?