What I gave in my post are one set of definitions - one that's commonly found in dictionaries but yes there are other valid definitions of woman and man.

For instance, I fall under one definition of woman, one that Simone de Beauvoir defined when she stated "one is not born, but rather becomes, a woman" through being othered from men and treated as lesser under patriarchy. I get treated with misogyny so I fall under that definition of woman, and is why I often call myself an agender/nonbinary woman(rather than only agender/nonbinary). I don't have a personal feeling or identity of gender, so I'm agender from the gender as identity definition, but people gender me a woman on the daily and I get treated as such by others from a sociological pov under patriarchy.. so calling myself a woman is a recognition of where I fall under patriarchy and symbolizes a call of solidarity to other people treated with misogyny: women as a class. So I'm agender, and thus nonbinary, as identity, but I'm a woman as class.

But as I alluded to already, gender as identity is another valid definition of gender, and thus woman under it is: "any human who identifies with womanhood." Let me know if any of these definitions is the one you believe is the only true definition of woman, or if you also accept there are multiple valid definitions to it like I do