@VanillaAndOrange
I never really thought about my gender identity before everybody started talking about it, but I wouldn't have a problem with stating that my gender identity is female. Just because that also happens to be my birth sex doesn't mean I don't see myself as female!
Gender identity refers to how well you feel the sex stereotypes and sex role stereotypes associated with one or the other sex align with your own preferences. Female is our sex. It refers to biology only, not preferences.
So, what you and me have in common with every single female human on this planet is our sex.
And we have many shared experiences arising from our biology with not just each other, but also with our foremothers and their foremothers and so on because of our sex. Such as a first period, which 99.5% of us experience naturally. Which also means that menopause is a nearly universal female experience (its symptoms are not). Or childbirth, which 80% of us do.
The preferences not so much. Especially because sex stereotypes and sex role stereotypes aren't even the same across time and space.
(For instance, a hundred years ago in the UK, a girl who wanted to wear pink would have demonstrated cross-gender behaviour, because pink was a colour for boys. Or 50 years ago a proper woman in East Germany worked full-time. Across the border in West Germany, a proper woman stayed at home.)
What you and me have in common with every female and male person on this planet is that we all belong to the same species.
But what do you and me and every other female person on earth have in common with males who identify as trans that we do not also have in common with all other males?
Can't be this so-called gender identity (in the case of males who identify as trans this signifies a liking for various stereotypes coded feminine), because I rejected those stereotypes while my age was still counted in single digits. Can't be biology, because they're of the sex evolved to produce sperm, and we're of the sex evolved to produce ova.
So what do all females have in common with this one subgroup of males that we can now meaningfully be combined into a new category?