'Self identification' of women can't make sense without some independent (sc. independent of self-identification) notion of what it is to be a woman.
Look:
Question: What is it for a person to be a women?
Answer: If someone identifies as a woman, then that person is a woman.
[That is what 'self identification' is.]
... That is not so much false as empty ; it is incapable of being true in any significant sense. It cannot be that what makes me an X is just my identification of myself as an X, whatever X is.
['I'm a scillion.'
-- 'Really, what's a scillion?'
'A scillion is just what people who say they're scillions are.'
-- 'Yes, but what is it that they say they are?'
'Scillions, stupid!'
--'Yes, but what does that mean?'
... And so on. And so on. For ever.]
The logic of this (its nonsensicality, if you like) tends to get obscured because of course we all know what a women is (what 'woman' means): a woman is an adult human whose sex is female (more or less - nothing hangs on having a precise definition just here). But you can't have that notion of a woman and self identification at the same time. And self-identification as a sole criterion for being a woman (or anything else) simply fails to make sense, as the above demonstrates.
So, a response to people who want you to agree with the idea that self identification makes one a woman is to ask them what a woman is: what, precisely, does the self identifier identify as? ('As a woman, stupid!' - 'Yes, but what does that mean?' ...)
What is a woman? My parents thought they knew; my grandparents thought so too; me, I used to think I knew what a woman is. (See above.) Now some soi-disant (pun intended!) 'trans' people think they want to change the meaning of 'woman'. We know what they want to change it from (see above). What do they want to change it to? They can't say ... because if they were to try to give the new meaning, they would have to deny self-identification. And self identification can't work without that new meaning. So self identification can't work.
I'm tempted to write QED. It really is that simple.