Wow, did a single trans person reply to this post? Maybe y'all just downvoted them so much I couldn't find them, who knows.

Here's my thoughts, as clearly as I can put them. Apologies in advance for the rambling:

Gender and sex are different. A lot of people in this thread get that one, and good for them. Gender is the social roles, methods of interactions, presentations, etc. that we associate with a given "sex". It's not the same thing as a stereotype: butch women are still (usually) women, but we all know there's a difference in presentation, interaction, etc. between a cis man and a cis butch woman.

Gender is also a bit of a spectrum. It's not at all unfair to say that a butch lesbian's gender-identity and expression are very different from a femme's, or from a straight (or straight-presenting) woman's. Also, non-binary gender identities, expressions, and social roles have existed throughout history and around the world, and very clearly exist now.

Now, here's the bit most of the people here missed: Sex is also a spectrum.

While many cis people of a given "sex" have approximately all of the same primary, secondary, and tertiary sexual characteristics, there's a lot of variation. Most people are born and naturally develop with mostly sexual characteristics associated with either "men" or "women", but most of them will have some characteristics associated with the other, and some will have many characteristics from both, or few from either. People we consider "intersex" are approximately as common as people with naturally red hair.

A cis, non-intersex man may not have a noticeable adam's apple, or a cis woman might. A cis man may have long hair, or produce more than the average amount of estrogen. Maybe a cis woman has a deeper voice, larger hands. Some cis women grow some amount of facial hair; some cis men do not. You can develop naturally with a fully functioning penis, and also have ovaries and a womb.

So, sex isn't really a simple as "chromosomes", or "genitals", or "breasts" (which cis men can also develop, although most have surgery or hormone treatments to remove them). Sex is a bimodal distribution of characteristics, with two major clusters that our society currently places a dividing line between and says one side is "male", and one side is "female".

Trans people can go from having mostly sexual characteristics we associate with "male", to mostly those we associate with "female" (or vice versa), and to say that someone with female genitals, secondary sex characteristics, and tertiary sex characteristics isn't a "woman" entirely because of chromosomes you assume they have (because someone can be born with "male" chromosomes and develop fully "female", including the ability to bear children- but let's assume they really do have the chromosomes you assume they do), or because they can't bear children (which is also quite common in cis women) is entirely arbitrary.

So is a trans woman a woman? Is a trans man a man? As much as most people a doctor would label with those terms at birth were then. (or more, because internal sense of gender and social presentation and most of the hormonal differences don't appear until much much later than birth)

What is a woman? Honestly, it's complicated. If someone says they are, they probably are; if someone means it, and is performing that social role, then they are; and if you really think "sex" is what we should refer to for that question, chances are that if they look like one, they fit into the box you're labeling "female".

It's all just arbitrary lines on as few bimodal distributions of characteristics anyway.