You only know your own gender. Society refuses to accept the existence of nonbinary genders, but that does not mean they do not exist. This is like saying, "I like chocolate ice cream but not vanilla, and I have heard that many other people do like it, so everyone likes either chocolate or vanilla!"
There are three: Male, Female, And transgender. People who are one thing but say they are another are not transgender, they are whatever they are, not what they say they are, but people with male and female parts are transgender, not male or female.
It depends on how you define gender. There are only two physical genders (male, female) (not counting birth defects), but there are more than two non-physical genders (male, female, transgender, and the like). Depending on which definition you use, the answer changes.
There are only two genders, and gender is not a social construct. Women have XX chromosomes and men have XY chromosomes--this can be seen even before birth. You can't possibly be another other gender because gender is not a feeling; it's biological.
The amount of people who identify as neither male or female is so small that it can be discounted as an anomaly. There is no utility in building anything on anomalies. It's good enough to say "other", for rare cases, and leave them alone. Truth is never absolute. Being 99% correct is acceptable.