Okay I'll do my best here im between sets at the gym, assuming that you have no background knowledge of quantum, statistical, and classical mechanics
1st thing to understand is that classical mechanics is derived from quantum mechanics, by the use of statistical mechanics. Originally, classical (aka Newtonian mechanics after Newton who codified them in Principles of Natural Philosophy) mechanics was held as inviolable, until the dawn of quantum mechanics 1st realized by Planck. This discovery was spurred by what was called the Ultraviolet Catastrophe, where classical mechanics yielded an absurdly incorrect result as compared to what was observed in experimentation. Planck fixed this by introducing a "fudge factor" number to make his model work (which then modelled thr phenomenon accurately). That fudge factor is now known as h, Planck's constant, a transcendental number. Rambling a bit, this led to Heisenbergs uncertainties principle which posited that particles actually do not have a defined position and momentum as classical mechanics states, but there exists an uncertainty in their values, where the product of this uncertain is greater than or equal to the reduced Planck constant, h-bar (h/2pi) divided by 2. Cool, nice.
Now, micro properties (such as individual atoms and molecules) had their behaviour explained by quantum mechanics, and classical mechanics was wrong. However, if you take a macro ensemble of particles and apply statistical mechanics, you end up at the limit towards classical mechanics. So classical mechanics will work on macrostates but not microstates.
Now let's explain this with a practical example, boiling water. You stick a thermometer in and it reads 100 degrees C. But since Temperature is purely a macro property, it doesn't actually exist in reality, only the summation of the individual kinetic energies of each molecule of water. This is analogous to Pressure, which also doesn't exist in reality. These kinetic energies of water are normally distributed (Gaussian) which means that some water molecules have high kinetic energy, while other molecules have low kinetic energy. The water molecules that have high enough kinetic energy to break the surface tension of the water surface escape as a gas. This gives the macrostate of a rolling boil, bubbling water.
Now this kinetic energy distribution also applies to every single molecule in your body. Biology is a macrostate of the individual chemical reactions of molecules in your body, a ridiculously complicated and ridiculously precise symphony of chemistry in action. However, since some, very little of these molecules have such a high kinetic energy (the very far end of the Gaussian distribution) that they'll react with things that they are not supposed to, breaking the activation energy. This is the fundamental reason why biological errors occur. One wrong reaction in the wrong place can completely change how your body functions.
Yeah physics is not my strong suit here but I'll take a stab at this. You made a good example. Water boils at 100 degrees Celsius, but only under the conditions we generally share on earth. If you were on the top of mount Everest or in a plane it can begin to boil at a lower temperature.
This is a perfect example of relative nature and why I think it's not as easy to say anything in regards to sex is definitive. If you know all this I would assume you could understand that.
I'll just assume in good faith you are correct as to why there are errors in human biology. But it doesn't change the fact that those aberrations do exist and can evolve. Just as culture does. So now if we can agree that intersex people exist. Clearly there is more to human sex than just male and female, because we do have evidence of true hermaphrodites capable of birth, I even posted a DOI link you can check out a few posts ago.
With all of this in mind why would you adhere to such a rigid gender definitions? I'm not even speaking about transgender people specifically. We know for a fact that asexual reproduction as well as hermaphroditic organisms exist.
My main issue is when people use the science of biology to deny the existence of transgender people because it's either intellectually dishonest or completely wrong.
And this is just me taking a guess because, again, me dumb with chemistry. If you are a chemist. What do you think about the possibilities of aberrations of brain chemistry that cause someone to identify as the opposite sex? If we discovered the chemical framework behind why transgender people feel the way they do would that legitimize it for you or not?