4 psychological genders:
Male
Female
Neither (schizoid)
Both
This explains why schizoids are emotionally aloof
What is the difference between physical gender and psychological gender? Well if I transplant a man's head onto a female body then he would physically be a female but psychologically he would still be male. In the same way a schizoid can have a male or female body but psychologically be neither male nor female.
I don't know how many sexual orientations there are though. Probably just 2.
As a result of trauma a normal person might outwardly appear schizoid to other people. This would more properly be called pseudo-schizoid. Just as a broken bone can be healed so pseudo-schizoidism is likewise curable.