Moore's paradox and gender

After just criticizing myself for being overly philosophical about trans people, I can't help myself.  Philosophy ate my brain, and anyway it's an attention hook.  Let's talk about Moore's paradox.

It is raining, but I don't believe it is raining.

or,

P, but I don't believe P.

The funny thing about Moore's paradox is that the statement might very well be true.  Sometimes, a fact is true even though I don't believe it.  On the other hand, if I actually made that statement, you would know that either I'm lying or that I think I'm lying.

As nonsensical as that is, sometimes people say something similar about gender identity:

I don't identify as a woman, I am a woman.

By saying that you're a woman, isn't that in itself identification as a woman?  What are we to make of this nonsensical statement?  What is the intended meaning?

In queer discourse, we talk about our identities all the time.  So sometimes I might say, "I'm gay", and the act of saying so is an act of identifying myself.  Other times, I might say, "I identify as gay", and that's a statement of my typical actions.  And there are a lot of nuances.  For instance, I might identify as gay on Facebook, but not in a job interview.  Or maybe "gay" tells an imprecise story about me, and sometimes I prefer to tell a more precise story.

I surmise that trans people are similar, and for this reason often talk about which genders they identify as.

Many cis people are privileged enough that they never have to think about their gender identities or the nuances thereof.  So when they see trans people saying they identify as X or Y gender, they see an opportunity to assert the superiority of their own gender identities.  The thought process goes, "All those trans women only identify as women, but I am different.  I am a woman."  But this is a fundamental misunderstanding of what is meant by identity.

I also learned that some people--feminists--have something different in mind when they say they don't identify as women.  They are trying to say that they don't identify with all the trappings of women's gender roles--pink dresses, makeup, shopping, homemaking, being overly emotional and caring.  This is a fine thing to say, but also represents a misunderstanding.  Trans women may also express discomfort with all the trappings of women's gender roles, or they may not.  Just like cis women.  When they identify as women, they aren't really making a statement either way.

This is all part of the myth that trans women always take femininity to the extreme.  And for decades, the image of trans women has been that of hyper-feminine women.  However, this image comes from outright erasure of less feminine trans women (as well as the rest of the trans spectrum), and also the medical barriers which basically required trans women to exaggerate their femininity in order to get life-saving treatments.