Hi. So other non-binary labels actually already exist, like neptunic and venusic. However, every queer label needs to encompass non-binarity, after all, one of the community's struggles is to accept all types of people who are not in the chap standard, which is proven when we realize that binary genders such as “man and woman” are, in fact, , white settler views on gender. In indigenous cultures, for example, non-binarity has always been present.
This is why the “female sex” is the “weaker sex”, because the term “woman” was created with the purpose of submission. This is also why many lesbian women, even though they claim to be women, are seen as if they “want to be men”, as “predators”, because in the end, labels such as lesbian and gay deviate from stereotypical gender rules: you can only be a woman if you perform femininity and are attracted to the opposite cis binary gender, if you do not fit into this pattern your gender (and your sexuality, if you are a straight woman in a relationship with a trans man) will be questioned and you will be ridiculed.
Understand that me saying this doesn't mean that I'm denying the feminine and masculine identities, these identities exist, heterosexuality exists, but these identities are part of an oppressive-controlling system that assigns gender roles to people before they are even born. Sexuality is linked to these roles, which is why it's so common to see gay men being called “women”, especially if they are feminine but still men, and yet their gender is questioned both because of their sexuality and because of their performance.
And more than that: feminine gay men are called women in a pejorative way, but if it's in fact a trans woman, people will soon see the man they don't see in feminine gay men.
This is why non-binaryism is included in strongly binary labels: because cis straight binary doesn't include queer people. Lesbian women, whether performing masculinity or not, aren't women enough for the cis straight binary, so much so that in many feminist movements they're expelled because they're seen as predators. The same goes for gay men in their given reality.
I will go further here and also say that transphobia, racism and misogyny are also interconnected. If you’ve ever seen the news about black (cis) women being beaten by men for being “mistaken for trans women,” then you know where I’m going.
So, if every person who deviates even slightly from the binary gender stereotype isn't their gender enough, then why exclude non-binary people from labels if what they represent is part of the counterpoint of the cis straight system? In the end, no matter how binary a queer label is, it will never be binary like chap labels, and that will always cause us violence. And that's why non-binarity is on every label.
That's also why we've reached the point where we realize that no one is born with a certain gender. As Simone de Beauvoir said: “One is not born, but rather becomes, a woman”.
In my case and that of many others, I didn't become a woman, but I discovered myself as a lesbian thanks to all my experiences in a heterosexual system. Therefore, excluding non-binary people, who don't identify with any gender, makes no sense: because binary (which we know) is, in the end, a chap model that queer and racialized people aren't covered by it.
Another example of how the West is influenced by the European binary, just look at how Western people react to Asian beauty standards.
This is also why the label pansexual, for example, currently has the same "meaning" (let's say this for simplicity's sake) as bisexual, because pansexual at the time the label was created with the intention of including trans people, and nowadays we know that all sexuality includes trans people, and bisexuality, like pansexuality, is about attraction to either gender (pansexual is still used and is super valid, just like any other label, because of its context and historical value).
Finally, non-binarity isn't a "third gender", something mystical that doesn't exist or that should be treated as something separate, which is why its inclusion in both transgenderity and strongly binary labels is also important, after all "what is it like to be a man?", "what is it to be a woman?", "how does this directly affect my sexuality? If at all."
I strongly suggest reading the texts of Leslie Feinberg, who was a butch lesbian activist who lived as a lesbian trans person in the 70s, so you can understand much more how the trans, non-binary and lesbian struggles go hand in hand, and get to know both more of the non-binary movement and how the chap system works.
Making it very clear that none of this is to say that “binarity doesn't exist”, but rather that queer binary isn't the same as chap binary, and it's a counterpoint to chap binary that goes hand in hand with non-binarity, just as the binary we know also does not include racialized people.
Seeing the world from a binary, white and European perspective is limiting and excluding. What isn't accepted is transformed until you understand that it's not about acceptance.