If you have a pair you're a male. If you don't, you're a female. Everything else is a phsycological disorder and needs to be treated. It's not that hard. Go to a farm and watch a horse being born. If it has a pair it's a stallion. If it doesn't it's a mare. If you cut the stallions balls off you have a gelding.
Not sure why this is so complicated.
Do you have a Ph.D in human sexuality? Do you also have a Nobel Prize in Medical Science? The great Alan Turing was incredibly gifted and has been credited with ending WWII vs. Nazi Germany, but by your 'deductive reasoning', he had a psychological disorder. We used to call such persons, mentally retarded, and yet, that doesn't seem to be a fair label here? Maybe it's more complicated than you say? Maybe you oversimplify because you're ignorant?