Did you get that definition of gay from Larry Craig or something?
I don't believe projection makes for universal truths. A lot of empirical studies have demonstrated that gay men don't react physiologically to the opposite sex. To say that there is no such thing as gay or straight is about as logically consistent as saying there is no such thing as blue or red because there are discreet intermediaries between each extreme. The alternative is that everyone be born a universal bisexual, a la Freud, but this idea has been debunked not only by empirical evidence but also the majority of personal testimony.
And then there is the lack of functionality or reflection of identity categories that your definition provides. There are men probably far more masculine than you who bottom, and there are nelly queens who are exclusive tops. And then there's the problem that a large percentage of gay men are versatile, or relationships between two tops that compromise sexually for the sake of the relationship, or gays who are only into frot or other forms of "equal" sex, or gay virgins who might not know what kind of sex they prefer, or couples that flip flop (are they jumping from being straight to gay and back by acting like that?).
Then there is the issue of culture or the homosexual as "species" as Foucault put it. Being gay comes not only with sexual preferences but a set of cultural spaces, traditions, and history that are distinct from the mainstream culture.
The Roman beliefs derive entirely from sexist assumptions that are as outdated as their approval of pedophilia directed towards slaves.