“Phobia” is of Greek origin, but it entered English via Latin. As I said, the word “homophobia” is cited by the OED as popping up occasionally to mean “fear or aversion to men/mankind”. This is obviously derived from the Latin “homo” meaning “man”. If we want to be pedantic about Greek instead then “homophobia” looks like it should mean “fear or aversion to things that are the same”.
But my point is that whether we’re going with Greek or Latin or (more sensibly) English usage, there’s nothing at all inappropriate or odd about the “-phobia” in “homophobia”. It’s consistent with centuries of English usage and Latin and Greek usage from long before that. What’s funny to me is that people who want to quibble about “homophobia” always go after the wrong part of the word. The bit that would be confusing to a time-traveler from ancient times or even the early 19th century is “homo”. They wouldn’t understand that in “homophobia” the “homo” refers specifically to people who are attracted to others of the same sex. But it makes sense in modern English, which is really all that matters.