I really like your argument here, because it really resonates with me as an ally. I could say a lot of things here about biological sex, intersex conditions, gender and how it differed from sex, all the usual stuff, yadda yadda yadda.

But here is the truth.
The world is better place when trans people are accepted. I know many, wonderful people, who contribute greatly to society, who would be dead now (or at least in an awful state) if they weren’t allowed to transition. These are good people, forced to live in hell, for reasons that are not their fault. And when they get to transition they are happier, I am happier, and our community is happier. You can give all the logic, all the science, all the facts, but it doesn’t help a trans persons dysphoria. It doesn’t reduce trans people getting attacked, murdered, bullied into the closet, or committing suicide.
Gender is a social construct. Guess what, we can change social constructs. Racism is also a social construct, and changing that leads to a better world. A world where we separate gender from biological sex, and accepts the natural variation that is trans people, makes the world a better place. It’s a social construct worth changing because it brings good. I accept and support the new gender theory because I’ve seen many lives improved by it, it does the world good. Let’s go there.

Here’s an analogy,

Logically, if I were to learn how to steal, and not get a job, I could get lots of money and become rich. That’s a logical fact and it’s true. True for almost anyone. So why doesn’t everyone just do that?
Well, if we all steal from each other, our entire society falls apart. So we made up a social construct of right vs wrong. Stealing is wrong. We live by these rules so we can have a functional society. But in a purely logical route, stealing isn’t good or bad, it’s just advantageous for acquiring wealth. Scientifically stealing could benefit me. But I don’t do it, because it’s wrong.
Accepting that gender is different from biology, is a new idea, a social construct, one that is beneficial to society because it saves the lives of trans people. I say we change this for the sake of trans people. Let’s have some empathy and understanding for them. Presuming them to not exist hurts them as well as our communities and society.