It's a way of legitimizing the whole thing, so e.g. rather than men saying "I want to be a woman", they can lean on this idea of gender identity and say "I am a woman", where "woman" has been redefined as "anyone with a female gender identity". And per the definition of gender identity, a man can be said to have a "female gender identity" if he wants to be a woman. Naturally, this redefinition has turned out to be quite controversial.
Nobody seems prepared to answer that question, yet it is a requirement to define this. Unless the argument really just boil down to "we make shit up as we go and you need to accept it or you're a bigot".
Someone may simply feel non binary as a high level and honestly descriptor of their gender. Which is to say that they feel the gender implied by their sex is a bad fit.
The existence of some people that take this to extreme labels that seem unlikely to be distinct and noteworthy classifications does not invalidate others who take more moderate steps that are probably genuinely more accurate assessments.
Would you also suggest we pretend the voices that a schizophrenic hears are actually there and real? If not, why not? It's real to them..