The reality is that TERF isn’t a self-given label, radical feminist isn’t a self-given label,
You're right, it's not a self-given label, and that's why when people decided that these people are actually not welcomed in feminist spaces, they changed the label to FART (Feminism-Appropriating Reactionary Transphobes).
Feminism, as defined by the majority of the movement, is about equality and intersectionality. If you hold exclusionary views you're not part of the movement, you're only appropriating the word.