You forgot the most obvious choice. There isn't a decent definition that fits with our intuitions.
Is a guy who has sex with a guy once, and girls the rest of his life gay? How about a guy who has sex with all guys, but a girl once? How about a 15 year old male who is attracted to other guys, but hasn't done anything? How about the 45 year old male whose always wanted to be with a guy, but who has a wife and 3 kids.
Especially because peoples intuitions vary between women and men. Two chicks kissing at a bar aren't necessarily considered lesbians by the people watching, but two guys kissing at a bar definitely are considered gay