It's weird that a gay man can say that he is gay, but a woman can't say she is lesbian. She says she IS a lesbian. amirite?

It's because gay used to be a word for happy. Like saying, "I'm Happy." But pretty soon the meaning changed and nobody feels like saying "I am a Gay," even though that's gramatically correct. The word fag is used there, and that's kind of insulting yourself so people just say "Yeah, I'm gay."

Lesbian can be an adjective and a noun.