The objection of Carson and the other rightwingers to the word isn't just invalid, it’s actually motivated either by marketing needs or lack of self-awareness (or both). For Carson, it’s the latter, while for the radicals in the professional anti-gay industry, it’s clearly the first.
The word "homosexual" was a portmanteau, drawn from both Latin and Greek. The word "homophobia", on the other hand, was a neo-logism, using "homo", a slang term for gay people, and "phobia", which is Latin (via Greek), meaning "an extreme or irrational fear of or aversion to something". It isn't, and never was, a clinical term, but rather one that was coined to label irrational anti-gay attitudes in public policy and politics. Ironically, it was coined in the first place because it was "nicer" than saying someone was prejudiced or calling them a bigot.
Times change, and language is neither static nor immutable, of course, and the term started to be framed by the rightwing as not just "wrong", but as evil. The professional anti-gay industry realised that if they didn't attack the term "homophobia", ordinary people might conclude that adults spending millions of dollars and their entire careers fighting to prevent their fellow citizens from being treated fairly and equally under law, including having the exact same right to assume the responsibilities and commitment of marriage, well, the people so against all that might be seen as mentally ill. But that's about THEIR image problems, not the utility, or lack of, for the term "homophobia".
The term was coined as a descriptor of irrational anti-gay attitudes in the public arena, and that hasn't changed. The fact that some people may use it more broadly, and some may now use it to imply a clinical meaning, doesn't change the fact that its core meaning hasn't yet changed (though, of course, it might).
And if the term makes the far-right extremists in the professional anti-gay industry squirm and feel they must explain that they don't really have an irrational aversion to LGBT people, even as they spend every waking moment and hundreds of millions dollars trying to prevent us from being treated with the same dignity and rights under law that they have as human beings, well, I just can't get upset about their discomfort. Maybe if they engaged in a little self-reflection they might realise WHY they're called that, and how, in fact, it's the perfect term.
Related: Radical right professional anti-gay activists are upset with Ol’ Ben because he didn’t stridently oppose equal treatment of LGBT employees by the corporations on whose boards of directors he once was once part of. He’s taking that as evidence that he’s not “really” anti-gay—he just doesn’t want us treated as full and equal citizens when it comes to protecting our families. Right…
This post is revised and expanded from a comment I posted on the AmeriNZ Facebook Page.