Why "homophobia" and not "sexualism" or similar?

From the etymology

homophobic

by 1971, from homo- (2) + -phobia. Related: Homophobe; homophobia

(which is said to date from 1969)

it points to the second meaning of homo, which is the slang version

comb. form meaning "homosexual," abstracted since early 20c. from homosexual

This can be read as a "phobia (fear) of homosexuals"

As @Mr Shiny's answer says, George Weinberg introduced this word "to refer to heterosexual men's fear that others might think they are gay"

Later Kenneth Smith was the first person to use homophobia as a personality profile to describe the psychological aversion to homosexuality.

Wikipedia states that this word was originally coined to refer to a straight man's fear that others might think he was gay. Its scope expanded to include all anti-homosexual prejudices within a few years when activists started using it. George Weinberg, a psychologist, considered these prejudices to be a literal fear and not simply prejudice. (Perhaps another way of looking at this is why isn't racism racephobia?)