Factually and biologically speaking, there's more than two. Lemme drop down on some history and science, here, so hold on.
So for starters, there's definitely no binary, it's just an oversimplification that is largely contextualized within Western culture. It's all a spectrum and you’ll find that reality is rarely as simple and as pure as uncompromising binaries. Gender labeling is very much highly contextualized by time and place as proven by the way different cultures have interpreted it. "Nonbinary" genders are definitely not some modern invention as the idea of nonbinary genders is as old as human civilization, because gender is socially constructed and subjective depending on origin, and people’s ideas about gender have changed over time and between cultures.
"And what cultures," one may ask. Well, here's to just naming some:
In Mesopotamian mythology, among the earliest written records of humanity, there are references to types of people who are not men and not women. In a Sumerian creation myth found on a stone tablet from the second millennium BC, the goddess Ninmah fashions a being “with no male organ and no female organ”, for whom Enki finds a position in society: “to stand before the king”.
In Babylonia, Sumer and Assyria, certain types of individuals who performed religious duties in the service of Inanna/Ishtar have been described as a third gender.
Inscribed pottery shards from the Middle Kingdom of Egypt (2000–1800 BCE), found near ancient Thebes (now Luxor, Egypt), list three human genders: tai (male), s?t (“sekhet”) and hmt (female).
The Vedas (c. 1500 BC–500 BC) describe individuals as belonging to one of three categories, according to one’s nature or prakrti. These are also spelled out in the Kama Sutra (c. 4th century AD) and elsewhere as pums-prakrti (male-nature), stri-prakrti (female-nature), and tritiya-prakrti (third-nature).
Many have interpreted the “eunuchs” of the Ancient Eastern Mediterranean world as a third gender that inhabited a liminal space between women and men, understood in their societies as somehow neither or both. In the Historia Augusta, the eunuch body is described as a tertium genus hominum (a third human gender).
The ancient Maya civilization may have recognised a third gender, according to historian Matthew Looper. Looper notes the androgynous Maize Deity and masculine Moon goddess of Maya mythology, and iconography and inscriptions where rulers embody or impersonate these deities. He suggests that the third gender could also include two-spirit individuals with special roles such as healers or diviners.
Anthropologist Rosemary Joyce agrees, writing that “gender was a fluid potential, not a fixed category, before the Spaniards came to Mesoamerica. Childhood training and ritual shaped, but did not set, adult gender, which could encompass third genders and alternative sexualities as well as “male” and “female.” At the height of the Classic period, Maya rulers presented themselves as embodying the entire range of gender possibilities, from male through female, by wearing blended costumes and playing male and female roles in state ceremonies.“
Andean Studies scholar Michael Horswell writes that third-gendered ritual attendants to chuqui chinchay, a jaguar deity in Incan mythology, were “vital actors in Andean ceremonies” prior to Spanish colonisation.
Two-spirit individuals are viewed in some Native American cultures as having two identities occupying one body. Their dress is usually a mixture of traditionally male and traditionally female articles, or they may dress as a man one day, and a woman on another.
In Pakistan, the hijras are officially recognized as third gender by the government.
Honestly though, if you want to see a little more in depth, Wikipedia summarized it nicely(since that's what it's for):
https://en.wikipedia.org/wiki/Third_gender
So moving on, there are three sexes identified in western cultures:
Female
Male
Intersex
So... there actually aren't even just two sexes/genders/whatever, just two primary sex
categories. Sex is actually determined by five categories, and while they're mostly the same for most people, that's not always true, and ignoring outliers is not really useful. We really only consider there to be two sexes because (supposedly) most of the world fits into two very identifiable phenotypical molds of male and female. They're not the only molds, though.
For AFAB people = XO, XXX, XXXX, and XY
For AMAB people = XXYY, XYY, and XX
Since the majority of the world's population doesn't get their karyotype examined, these chromosomal quirks are more common than we think. And considering how these specific combinations
don't always come with the associated symptoms, we might not know if we even have them. So one could have one of the aforementioned combos without knowing it, which is why it makes no sense for binarists to strictly believe that every woman must have XX and every man must have XY to be a "real man" or "real woman."
I should also point out that hormonal patterns for AFAB XX people
can naturally and biologically mirror that of a typical AMA XY person, or vice versa, which gives rise to things such as AIS(Androgen insensitivity disorder) or basically an intersex condition. And does this cause any health risks? Nope. But the influence of the "There's only XX and XY" binary does, as it causes harm to intersex children(
http://www.isna.org/faq/standard_of_care), as they're forced through harmful surgeries and hormonal treatments just to make them "normal" or a "real boy or girl."(
http://www.isna.org/faq/concealment)
People may also say "Uh, that doesn't count, it's a disorder!" Which is pretty funny. This magical gender invalidating power of "disorder" only applies to people who happen to be born threatening the binary. These people might not even come with the associated symptoms(as I've said earlier) but they're still disqualified, which is circular logic at its finest. Also, they forget that classifying it as such may risk their lives and livelihood. People kill the disabled, people deny us rights, we can lose jobs and lose family and friends, we can become targets of harassment. Of course that doesn't matter to those who like to keep the status quo, though.
I'd also like to point out that sex differentiation in humans isn't even controlled by chromosomes as much as people think, our development is mainly piloted by our hormones. Chromosomes play a very small part in development. Kinda wish people would except that nature is more complex than what someone learned in a fifth grade bio textbook, and that chromosomes can't tell someone's "real gender," technically speaking.
So what's happening now is that essentially people who don't feel content with "Male" and "Female" as labels are creating new labels. So in many ways, yes, there are infinite genders, because no two people are likely to have the same feelings about who and what they are. Like all taxonomy, though, there's still a need for definitions as opposed to just "avoiding labels".
For a metaphor:
Are you familiar with the concept of scientific Taxonomy? The branch of biology dedicated to categorizing different types of animals. Species, genus, order, kingdom, etcetera?
A lot of people consider taxonomy to be some kind of biological objective truth, but the fact of the matter is that life itself doesn't exist in neat divisions. Taxonomies change and classification shifts as new understanding arises. The Red Panda has been placed in the Racoon and Bear Family at various points, but now has its own Family (Ailuridae) for instance. Ultimately nothing changed about the red panda, just scientist's understanding of it. The term "Ailuridae" exists solely to be used to talk about the red panda, and doesn't actually mean anything.
Likewise, canis lupus familiaris is just a term used to talk about and categorize dogs. Dog breeds are also very visible, so we'll stick with that metaphor for now. Think of gender along these lines. Think of each of the genders as a different type of dog. You can go down to the particular breed, and categorize things so you know the difference between a Border Collie and a Rottweiler. And, of course, you can go even further and refer to a specific dog by name. You can get that specific with gender, too. Which is where a lot of those hyperspecific terms come into play.
But unless you're a dog breeder, chances are you're going to call them all "dog", or maybe know a few. You might know a collie, but you won't know the difference between a border collie and a rough collie, and you don't need to know the difference.
My point is that people like to make arbitrary categories for anything and everything, and gender is no different.
Now, even if gender was the exact same thing as sex, it still would be neither binary nor a scientific absolute. In her novel "Sexing the Body", Anne Fausto-Sterling(Professor of Biology) explains that there are 5 specific measures of “biological sex” according to modern medical science:
1. Chromosomes (male: XY, female: XX)
2. Genitalia (male: penis, female vulva and vagina)
3. Gonads (male: testes, female: ovaries)
4. Hormones (male: high testosterone, low estrogen, low progesterone; female: high estrogen, high progesterone, low testosterone)
5. Secondary sex characteristics (male: large amounts of dark, thick, coarse body hair, noticeable facial hair, low waist to hip ratio, no noticeable breast development; female: fine, light colored body hair, no noticeable facial hair, high waist to hip ratio, noticeable breast development)
In actuality, very few people actually match up with all five categories. estimates by the intersex society of north america notes the frequency and prevalence of intersex conditions, and puts the total rate of human bodies that “differ from standard male or female” at around one in 100, while Anne Fausto-Sterling estimates that 1.7% of the population do not fall within the usual sex classifications. However, both of these estimations are somewhat outdated, so it could easily be a much higher percentage.
TL;DR: There are people out there with XY chromosomes, testes, a vulva, a vagina, “female” secondary sex characteristics, and “male” hormone patterns; people with XX chromosomes, testes, a penis, “male” secondary characteristics and “female” hormone patterns, and there are even people with both “male” and “female” secondary sex characteristics or hormone patterns at the same time, regardless of their genes, gonads, or genitalia. Now, these people are technically intersex assuming that the two sex system is absolutely true. However, in order for the binary to even be considered real, every single person on earth must completely match up on all 5 markers of sex all the time. That’s not what happens in real life. In real life, literally tens, if not hundreds of millions of people have bodies that are contrary to the biological concept of the two sex system. Yet, folks prefer keeping the status quo over allowing a new concept to take over that could save folks' lives and such.
There's my few dollars.