I've never been a fan the term "homophobia." Unlike terms like "racist" or "sexist," the word "homophobia" implies that gay people are to be feared. It makes hatred of gay people seem less like bigotry and more like caution.
Further, it implies that bigotry against people who are gay, lesbian, bisexual, or transgender (GLBT) is different from other "-isms"; racism, sexism, and agism. These words are associated with hate and bigotry, generally accepted to be bad things. Phobias, on the other hand are neutral things, they don't reflect badly on fearer.
And of course, the term itself doesn't make sense. The prefix "homo" means "same," so "homophobia" isn't fear of homosexuals, it's fear of "the same." Actually, maybe that does make sense. Perhaps so-called homophobes are afraid that people who are GLBT are, in fact, equal to them. Maybe homophobes are afraid that people who are GLBT will live in the same neighborhoods as them, go to the same schools, have the same rights. Maybe homophobes are afraid of finding out they're not all that different than the folks they hate.
Or maybe homophobia is a different animal from hatred of gay people. Maybe homophobes are just folks who are afraid because they don't understand. Or maybe they're people who have been taught to fear people who are gay and haven't yet learned any different. I mean, I was afraid of sushi the first time I tried it. That may be a bad example since I hate sushi, but I think you get my meaning. Maybe calling someone a homophobe rather than a gay hater means there's hope for them yet. Or maybe calling someone a homophobe is an unfair label. Maybe we should use people-first language and call them people who are afraid. Or maybe I'm rambling.
The Internet tells me that the term first appeared in the late sixties or early seventies, and every etymology site out there credits another person for coining the term. And it probably gained traction due to the fact that "homoism" and "gayism" sound fairly silly. I've heard "heterosexism" and "sexual prejudice," but I think the best way to resolve the issue is to eliminate the sentiment.
Maybe we should change the vocabulary of hate altogether. Maybe we should just call hate hate. Racists aren't racists, they're people who hate. And heterosexists are people who hate. And sexists are people who hate. Perhaps that makes me a hatist.