To state that someone is "Homophobic" means they are afraid of gay persons. But people aren't afraid of gay people , they are plain disgusted because it goes against all traditional morals and values . So gays are considered abnormal . The word " Homophobic" is a made up word to place a specific blame of someone and I can't stand that fake word . If someone doesn't like me because I am a lesbian then tell me ( and they do) but I won't call them "Homophobic" because I don't think they are afraid of me . They see me as abnormal and out of social normalcy .
As for Mew's dad you can see he is NOT "Homophobic" but just plainly sees her as abnormal and disgusted because males and females by design are supposed to pair up and become life partners and have children . But because Mew isn't a normal woman who takes a male as a mate she "will not" have children and that makes her father mad .
The suffix "-phobia" has a primary definition that denote a fear, but it also has a secondary definition that denotes aversion or repulsion. This is the definition in play in the word "xenophobia" (aversion to foreigners), "homophobia" (aversion to homosexuality), and when talking about hydrophobic materials, which repel water. This is part of the "wonder" of the English language that some words or word particles can mean more than one thing.
And it's funny whenever someone goes all etymological on the word "homophobia" they always single out the "-phobia" and never the "homo-". If one wants to get linguistically reductive, "homo-" just means "same". So "homophobia" should really mean "fear of the same". But no one goes around saying "Gee, I'm afraid that tomorrow is going to be just like today, so I must be homophobic!"
Words are more than just the sums of their roots, especially since the definition of those roots drift with time and usage. Just look up "anti-" in the dictionary. Lots of similar, but significantly different, definitions, depending on what the prefix is attached to.