My brother asked me about this the other day. His coworker's daughter pretends she's a cat and he wanted to know why we shouldn't just let her identify as a cat if we let male individuals be women. I told him that the difference is that only one of these things is actually physically possible.
Of course he tried to say that 'no, it's not possible for a male to be a woman', but I asked him to really think about it. If a little girl draws whiskers on her face and runs around in a kitty ear headband, you look at that girl and think 'Oh, she's a little kid pretending to be a cat. You don't see a giant mostly-furless cat.'
If in the 19th century you had a penis but knew you were a woman, literally all you had to do (simplified for the sake of the argument, mind you) was affect a falsetto, wear a skirt, grow your hair, and diligently shave your facial hair. That's all. People looked at the way you presented yourself and assumed you were a woman (because you were).
I don't think he realized the difference between sex and gender. Once I laid it out as something done even in the past, something possible even without modern surgeries, he stopped arguing to think about it.
Keeping in mind, this is a man who has trans coworkers and his opinion of them up to now has been 'Why should I care about what's in their pants so long as they do their jobs?' So, I think he's been listening a bit too much to conservative propaganda of late.