Must disagree here. Yes, we have, historically, created a plurality of classifications of sex, based on the principal of "two commonly occurring". But this is based on a historical lack of knowledge. The fact that we don't commonly use any other terms doesn't deny the existence of intersex people, nor does it deny the fact that classifying them into rigidly male and female categories is unfair at best.

Also, your "p and not p" argument only works simply because it is being applied to a binary system. If you have more than two options, then "p and not p" does not suddenly turned 10 options into 2. It can be used as a classification in a valid context, but it does not make the possibilities binary.