Do you understand the basic difference between the terms sex and gender? It seems that the confusion ITT revolves around the issue. Here is an accessible video on the topic:
I'm just relying on peer reviewed, published research to support the claim that sex is not a simple binary opposition between male and female. See James, Rose et. al. (2011) in the American Journal of Medical Genetics - "High-level 46XX/46XY chimerism without clinical effect in a healthy multiparous female."
The idea that gender is culturally determined is not something I'm just making up to prove a point on a reddit message board. The very meaning of the term gender acknowledges that is culturally determined - have you bothered to look it up? We don't talk about languages having grammatical sex, but grammatical gender, because gender is only very loosely (if at all) associated with notions of sex. It would be absurd to claim that a word or grammatical ending has a sex, precisely because it's a biological notion. It's not absurd, however, to claim the existence of grammatical (or human) gender, precisely because it isn't determined by biology. It's almost tautological to say that gender is culturally determined.
Here is a pithy summary of the current (as of 2015) state of biological research on the idea that sex is not a simple m/f binary:
Good luck with your argument. Almost a Sisyphean task to try to make a point like this in southern Indiana, tho.