The right to mis-define oneself

[henryp]

Accepting her as a woman and her actually being a woman are not equivalent.

No, they're not. She is not a woman in the most strictly biological traditional meaning of the word that Pyr brought up, we know that. But she is female and if you're not an asshole seeking to deliberately cause her pain, you won't be pointing that out to her all the goddamned time.

Why are you so bothered by this?

So, I think where some of us are getting tripped up, is that as "atheists" many of us are all about the whole measurable fact department. So when you say "She's not in the most strictly biological...", that's how many of us define male/female.  Strictly biological.  
And the rest, to some of us, is immaterial.  I think it's, interestingly, associated with the movement to remove gender stereotypes.  If this were 1950, when women were still in the little box of how they were supposed to behave, then it'd probably be a lot easier to accept.

Instead, we have a culture that rightly (i think) believes a man or woman can do whatever they want regardless of if they are a man or woman.  Femininity and masculinity are no longer factors.  Sex with the opposite sex isn't a factor.  Liking musicals, being in touch with your feelings, punching people for a living.  It's all wide open.  A woman can be anything.  A man can be anything.  

So now we have a man who says "I identify as a woman."  But there is no longer a "woman" identity in some of our minds.  So it's like the Transgender stuff is lagging 20 years behind our current views.  For some of us, the labels of "Man" and "Woman" only exist as strictly biological identifiers, so we're having a bit of difficulty figuring out what exactly is being talked about.