So - that last category sort of does it to mark their being a person, not a gender? Maybe that's the point, to state it simple: that people are not their gender, but some species behind it, and that they could perform anything, and that their 'natural' gender is no more natural to them than the other gender would be.
Thing is though that gender is not really thrown away if people go perform part of the other gender, as they do it with the intention to take things over from the other gender, and the parts can still be recognised as parts of different genders. So concretely: if I (female) would have very short hair and wear a necklace with pins on it, plus a skirt, people would think the skirt female and the hair and the necklace male. And with other behaviour than dressing, the same. So the binary isn't overthrown then... Maybe that's what my teacher meant.