The confusion here is that saying "I am a woman" simply *is* expressing a gender identity - it reflects having a "sense" of which sex one belongs to, whether that is rooted in "morphology" or otherwise.

If you follow the link in your quote, it's clear that the people that actually use this as a slogan are not in fact people who are "agender or genderfluid”. Similarly, people expressing a sexual orientation can't claim to be expressing an asexual identity - “I don’t have a sexual orientation, I’m just straight” is equally absurd.

Likewise, in your "size identity" example, clearly the first individual doesn’t see themselves as “sizeless”.

Yes, I think there may be aspect here of "fish don't know they're in water" which can make dialogue about gender difficult. But in reality, my experience is that most people don't find "gender identity" conceptually difficult.