Well they're not saying anything incorrect there. The concept of gender identity was only invented to try to provide some cover explanation as to why some people want to be the opposite sex.

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.