“homophobia” doesn’t even have Greek roots.
It has one Greek root, “phobos”, which originally mean fear but has over the centuries come to mean fear or aversion; and one English root, “homo”, which is short for “homosexual”, which has one Greek root and one Latin root.
It means “aversion to homosexuals”, which is unusually apt for its derivation.
People, homosexuals included, should make more use of sources such as etymological dictionaries before they mechanically repeat current usage, which may well be erroneous.
Current usage is never erroneous, since the meanings of words change over time and are determined by their current usage. Current usage may be sloppy, ungrammatical, ambiguous, or even contradictory, but it cannot be erroneous. Using etymological dictionaries to determine the meaning of words, rather than just their derivation, is a really bad idea.
For an excellent example, the etymological root of “current usage” suggests it means the same as “running practice”.