Actual Discussion

OK, so I did a bit of research (as is my obsessive self's wont) and can answer for "gender".

Our modern understanding of sexual matters is far more subtle and nuanced than the old-fashioned notions most of us grew up with¹. What follows is a simplified take on things. The reality is more complicated and has many more axes than I'm highlighting.

At the lay level you can think of there being three axes of sex-related issues:

1. Sex. This is whether you're dangling wedding tackle or not. Your physical sexual characteristics.
2. Orientation. This is the sex (or, more broadly, gender for which q.v.) you are attracted to for sexual activity.
3. Gender. This is the mental model you have of which sex you are.

Gender is in most cases oriented to match your sex (cisgender) and in opposition to your orientation (heterosexual). Because, however, the body, and various parts of the brain grow at different times, it's possible for these three axes to differ due to hormonal differences in the mother's body (external factors) or to activated genetic influences (a mix of external and internal factors). If one of these factors activates at one point in development, the part of the brain that regulates sexual desire flips the switch and your orientation is different². If one of them activates at another point in development, the part of the brain that models your internal view of your sex flips and you now have that thing called "gender dysphoria".

And after literally centuries of trying to "fix" people with gender dysphoria through abuse, through religious counselling (c.f. "abuse"), and through therapy, it's pretty much well-established that gender dysphoria has no talking (nor abusive) "solution". Thus the kindest thing to do is to let people whose gender doesn't match their physical sex to present the gender they feel themselves to be by behaviour, manner of dress, and ultimately, as far as is practical, physically. Anything else is abusive and cruel.

Note, again, I stress this is the very simplified model, and it's filtered through my inexpert, non-practitioner understanding of things. (I'm open to correction by those with actual expertise in the field, obviously!) As such it doesn't address the huge forest of orientations (which I alluded to in the footnote below), it doesn't address intersex issues, and it doesn't address gender issues like the "non-binary". And indeed I don't, to cite Orwell again, "bellyfeel" gender dysphoria, enbies, aces, etc. … but in the end it doesn't fucking matter. There is literally zero impact on me if someone wants to call themselves "non-binary" or "trans" or "ace" or whatever. So even if I don't "get" it, what I do "get" is that these people are profoundly unhappy in the circumstances they find themselves in and if transitioning helps them, all the fucking power in the world to them!

¹ Why "most of us"? Because there are cultures out there that have more nuanced models than the strict binary. Look up terms like "hijra" for the Indian sub-continent, the role of eunuchs, M→F gender-swapping actors, and F→M cross-dressing characters in heroic lore in ancient China, the กะเทย/kathoey of Thailand, the whole allure of "fox spirits" all over the east Asian sphere, the "two-spirit" peoples of North American natives, etc.

² For instance that part of my brain flipped me to a "2" on the old-timey Kinsey scale (nominally heterosexual), though on more modern classifications that the kiddies would use I'd be a het-leaning pansexual.