It's only illogical if you never carefully thought about the difference between a concept and a human being. Between the ego and your essential human essence.
Celebrities are a good example because they have larger-than-life personal brands (concepts) that often obscure their humanity. For example, a superstar like Beyonce is associated with certain concepts in people's imaginations: glamour, sexiness, icon, being a diva etc.
She's so heavily associated with these things that people might use her name as a substitute for saying these words. They might look at an outfit and say "That's so Beyonce" or a way of dancing, behavior, and movement and say "That's Beyonce-esq".
Yet, if you were to take it one step further and say "I identify as a Beyonce" people would find it odd. Because they recognize that although Beyonce is heavily associated with some concepts, she's also a distinct human being. And to" identify as" her is almost like saying she's more of an idea than a real, living breathing person.
Yet, this is precisely what the concept of gender does to women. It takes ideas and aesthetics commonly associated with female human beings (softness, feminity, wearing dresses, certain hairsyles, nurturing a child etc) and uses those things as a substitute for actual living breathing human females walking this earth. This is the reason why gender has been defined as a tool of sexist oppression wielded against women.
To "identify as" Beyonce Knowles-Cater I would have to first remove her humanity (her distinct human thoughts, emotions, ideas, livingness, beingness) and flatten her into a concept, an idea, behaviors, styles of dress, movements that I can embody.
This is what every male who "identifies as" female does. Without exception. And it would be one thing if they did it to cope with some mental illness. But now "You don't need dysphoria to be trans". It's the normalization of female dehumanization.