The idea of sex being binary is based on the idea that male and female are not only black and white, but also many shades of gray. But each of those shades of gray are still either male or female; each shade does not have it's own name.
The part I put in boldface seems to contradict the claim that sex is binary. The different "shades" of intersex categories can have any names we choose to give them, and specialists who study intersex produce names for categories that make sense to them. However, it is important not to confuse the biological concept of intersex individuals with sexual orientation and gender dysphoria, which may have nothing to do with the gonads that one is born with.
Gender pronouns can be be confusing, because they represent an arbitrary social distinction that can change over time. As I've pointed out before, different languages have different conventions regarding gender reference, but we've just been discussing English conventions here. Some languages make more distinctions and some fewer. English is not as bad as most European languages in terms of forcing speakers to make gender choices that may not comport with reality. The problem is that social and linguistic conventions do not always match up ideally with the real world.
If there are a variety of sexes, each sex should have a name. She mentioned Male, Female, and Intersex. If there are more, what are they?
You can find this information on the internet without me having to cut and paste it here. I suggest you start with Wikipedia's page on
Intersex. There are a lot of names for categories that are more specific to the male and female ends of the scalar range, but some (for example, "true hermaphroditism") are neither. If you look under the
Prevalence section, you'll find a table that also gives statistics on prevalence in the general population.
Again, we need to be careful not to confuse intersex conditions with sexual orientation, which is orthogonal to biological sexual characteristics.
Gender dysphoria is not just about intersex individuals.