No hate, but I love a good debate if you're up for it.
Scenario 1:
Great points, honestly. However, even in this scenario where someone manages to cover all of the bases and managed to create an exact list of what it means to be a woman, it would be impossible to disqualify trans women.
Scenario 2:
I'll get deeper into this one since it's more realistic.
I bet you can't define a car
Vehicles are defined by their frames, and the regulations that revolve around those. I can tell you with absolute certainty whether a vehicle is a car or a truck based off the frame. But this isn't the point.
Does that mean we all just get to [define words ourselves]
Actually yes. Words gain their definition by how they are most commonly used. You learn a word based off its definition, but the word gains its definition from use. This is how Shakespeare managed to invent so many words in English. He just started using them, and when people asked what they meant he told them and they started using them. This is also why "literally" is defined as "not literally" by Webster dictionary, or at least it was around 2016 (may have changed).
As a matter of fact, entire languages have been built around this concept of redefining words. Most of German is just portmanteaus that were understandable enough to be considered a word.
In this particular case, the words "man" and "woman" is slowly being redefined by society to be more inclusive of trans people. Fighting against the progress of language, in this scenario, is nearly identical to fighting against the progress of trans people.