Gender is the attempt to capture the spirit in a category, or sign. Generally the subgroups of society have decided that the spirit can go in two directions, but sometimes a culture decided things weren't so simple (see māhū or hijras or the plethora of others). Gender was perhaps the first sign. This makes it difficult to ask why exactly it originated, but we can see that this sign gains power by binding together collections of individuals, much like race or culture.
I am a trans woman, and because of this, I am expected to have a strong sense of belonging to a gender. The "trans" here in its most essential form signifies the desire to move from one sign to another. But now, through the creation of "trans," a new sign under which a shared experience is innate, there is now the "trans woman," and this too is, in some sense, a gender -- at least in its relation to the primordial binary, at most in its monolithic definition of our identities by greater society. The content of the sign of "trans woman" contains so much now that its difficult to compress. One story, though, resonates: I was told from birth growing up that I am a boy, and now I want to take estrogen. That is my own personal identification with the sign.
The most woke among us might say: "Are you not closer to agender or nonbinary?" But they say this without realizing that those, too, have both become genders, mostly defined by having piercings and somewhat embarrassing names. Signs are weak and malleable compared to the expressive force of humans. This is the element conservatives attempt to exploit when they talk about men in dresses, in your bathrooms, speaking to children, having fetishes, etc. It's easy to weigh down a sign in characteristics external to those that bear it, particularly when those who attempt the former greatly outnumber the latter. Through this, inevitably, the sign of "trans woman" will be destroyed, as the sign either bares such little reference to reality that it no longer applies to anyone, or those under the sign are punished for bearing it.
What all this does not explain, however, is where gender as a sign draws its power and relevance in society from. How can such a varied sign, which now points in a million directions as its soaked up three thousand centuries of characteristics, be of any value? The power of a sign is relative to how accurately it can depict reality. Once, in the valleys of Central Europe, there were Bavarians and Prussians and some people on the Rhine and some on the Elbe. However, in the 19th Century, through language and constructed mythology, some new sign was born in the collective imagination that depicted reality so transparently that it quickly came to sit above the regional identities that was called "German." But why Germans still call themselves that is not this clear. Not all Germans view images of Europa in their sleep or have some unspeakable bond with Bavarians, but perhaps just speak German, or were born within the Federal Republic of Germany. The nature of the group changes over time as the characteristics of its sign vary in their ability to describe the group.
Perhaps male and female still speak to some essential truth, the forbidden shopper gland or the hole-in-wall compulsion, but it seems more likely that it accurately captured a social relation, that of patriarchy. This is supported by matriarchal societies generally also having third gender roles, signs of gender changing to depict a separate hierarchy, though third gender roles were certainly not limited to matriarchies. For many, though, they speak of one ultimate truth, the biological truth. The sign of the penis and vagina, the phallic and the yonic, are definite, and perhaps the -1st and 0th signs. The first gender we are all assigned is based on this. When comedians talk about trans women, they can't help but start talking about penises. But the phallic and yonic have become increasingly challenged as gender's plethora of characteristics have proliferated. In daily society, gender has become a look, a sound, a way of movement, of acting. As the phallic and yonic gradually untether from the binary, the signs expand and fracture, and thus, the crisis of gender, or rather its new form. Bodies no longer need to change for their gender to.
What is gender euphoria in the world of arbitrary signs? Remember that gender is an attempt to capture the spirit. The spirit, as an intangible but at some level present object can only be quantified in signs. So, it is only natural we find it rewarding as a sign gets closer to describing our spirit. To be removed of any sign that can reflect your spirit is seen as one of the great indignities one can do to another, the idea of completely uniform masses with no inner sense of self sending images of gulags and hell into the American psyche.
It is more than a label, but it is constructed, and its foundations in the human form have already begun to be subsumed into new signs (AMAB, AFAB). Are trans people inevitable? Yes. Not because of the unstoppable march of social progress, but because of the internal contradictions within the sign of gender.