short for homosexual (n.), attested by 1929, usually contemptuous; as an adjective by 1933.
[H]e imported a whole boxcar of broncos from the West, homophobic mustangs, as it turned out, that nobody but a rodeo hand could have ridden. [F. Reid Buckley, Life Magazine, 1970]
The "fear of homosexuals" sense is attested by 1969, from homo- (2) "homosexual" + -phobia + -ic. Even early on the term was used with a tinge of "unreasonable or abusive fear of homosexuals" and in current use it typically implies or asserts an active hatred. Related: Homophobe; homophobia
"having the same position, value, structure, etc.," 1650s, from Latinized form of Greek homologos "agreeing, of one mind," from homos "same" (see homo- (1)) + logos "relation, reasoning, computation," related to legein "reckon, select, speak," from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak (to 'pick out words')."