I don't know what this means really. How does biology tie a sense of self to external circumstances? Can you say more about this?
I guess the easiest way to explain it would be to say that culturally certain personality traits or ways of expression are coded as "feminine" or "masculine". Certain ways of speaking or dressing would be read as "feminine", regardless if they are exhibited by a man or a woman.
GC view perspective would most likely claim that this is just a cultural product, and that these are just "human traits" that everyone should be free to express anyway. Which is true in my view.
However these "masculine" and "feminine" traits are so strongly associated with being either male or female, that they are synonymous.
From the GC perspective no sex has a monopoly on the traits coded as masculine or feminine. Everyone should be free to express themselves any way they want to. However in the real world the traits categorised as "feminine" reside with the category of women, and the traits categorised as "masculine" reside with the category of men.
This has the effect that you cannot be a fully and legitimately feminine person without also being a woman. In other words, unless you present as a woman, you will not be be seen for your "most authentic self".
(The notion of "authentic self" has to be questioned most likely, together with the need for external validation of it, but I will leave it here as part of the argument).
So all the people who strongly identify with their traits commonly coded as "feminine" or "masculine" will feel threatened if the categories of of "man and woman" are hinged on biology, because they will not be able to inhabit the only categories where they can legitimately be "themselves" on the strength of their gender-coded characteristics alone.
And outside of that category they will feel illegitimate/invalid, because only being in the category "woman" makes ones "feminine" expression valid.
It's a little bit like the obverse side of the "you aren't a real man because you behave in an unmanly way". It is "you cannot be true to yourself and express it in away that is perceived as valid, unless you are a woman".
These personality traits are valid in themselves, and they are independent of sex. And they exist.
But because they are socially coded in a gendered way, and because the person having them identifies with them in a gendered way, they can only be expressed in a way that the person feels is legitimate in the gender that is the "home" of that code.
If we then say that being a woman or man hinges purely on biology - this threatens all those who view themselves as essentially feminine or masculine at their core.
They have learned that their personality is gendered. They feel they cannot express their personality outside of the gender category to which similar personalities are assigned culturally. And then that category gets defined purely on who has which genitals. I think it can feel like a really strong attack on their sense of self, because it is saying that they lack the physical trait necessary for them to be able to legitimately live out their authentic self.
And then the people who grew up with the gendered view of their personality traits, who are at home in the sex they are born in, will feel that they are a man/woman at their core (because of course their personality exists). This will lead to a feeling of reduction, and also invalidation, because they will feel that their inner sense of self is also invalidated through them being seen as a man/woman purely on the basis of their sex.
I mean... we all try to conform to these expectations, and people actually put a lot of work into it. Men try to "be a good man", to be "strong and honourable" and whatnot - to do all this work to be seen as a "real man".
To say that a "you are a man if you have a penis", will feel invalidating to them too.
That's how I understand it anyway.