No, you do not understand what I have said at all.
I am a woman.
This is not my "identity" in the personal sense of self that could somehow be "cancelled". It is certainly not, despite what trans people believe, something to do with how I think.
It is a simply fact about me in the same way that my shoe size, my height and my intelligence are. However, unlike my my shoe size, my height and my intelligence, it is something about me that is discriminated against in our society both in large, structural ways like the childcare burden and unconscious bias in employment, education and culture, and in intimate, personal ways like how men (not all men, but enough men to matter) feel entitled to speak over me, demand my attention, and at worst physically or sexually abuse me.
These things are true. They happen. They happen to us because we are women. If there is no language to name ourselves as women they do not stop happening, we just lose the ability to describe it, identify the patterns and puts laws and other mitigations in place.
When you give away our language, this is what you give away. And you give it away for no other reason than to make people who are deeply sexist, so sexist that they think men and women have to think a certain way, "happy". You might value other women so little that you think that is ok, but I do not.