Does it annoy আপনি when people are called homophobic when they are not?

Yes, it bothers me quite a bit actually.

I think- while understandable -the word "homophobic" is being used a little too loosely. People often go to that conclusion before hearing what the other person has to say. Often times, like your friend, they're a little uncomfortable about the subject, but that doesn't necessarily make them hateful towards homosexuals. It usually means they aren't used to it, and it does take a little bit to understand. A lot of the time, these people who are uncomfortable with it are trying to become আরো tolerant- and that is sometimes a process. It doesn't make them a bad person if they aren't as open minded at first, but it isn't to say that they never will be accepting.

Calling someone "homophobic" অথবা "hateful" when they aren't full-out expressing hate can be damaging, and makes us look like close-minded radicals. We're trying to spread tolerance for everyone, but calling someone out doesn't display that. It's not a black and white issue. I do think that this "discomfort" can only go so far though, like if a restaurant owner feels too "uncomfortable" to serve a gay couple. Then that's discrimination, and it's up to them to put their prejudices aside and behave like a grown up.

I wish homophobic wasn't such a commonly used term. If we continue to react aggressively to every little differing of an opinion, it won't help our cause. If someone goes up and says "fag" "dyke" "eww" "Adam and Eve, not Adam and Steve" etc, then I think they could use a little bit of a word slap. If they seem a bit confused about it, I think it's better to slowly ease them into it- explain your opinion about the matter, but don't chew them out.

If that makes sense.

I'm sorry, either you've been পাঠ করা the wrong dictionary অথবা talking to a psychologist that isn't in their right mind.
A phobia is an irrational fear অথবা someone অথবা something, homophobics don't necessarily hate they're just afraid. নমস্কার if you're going to make fun of homophobics, at least get your facts right. Screw you!