Koreans seldom call those who are older than them by name.
The guy called 오빠 by your friend is older than you? Then how do you usually call him?
Is he a native Korean, half or a second generation?
Sometimes, it could sound too intimate when a young girl calls a older guy 오빠 as if she is his girl friend. This might be one of the possible reasons why he got angry when he was called 오빠 by her. Having said that, it is an appropriate and natural way for a young girl to call the older 오빠.
She should never call him -아 because it is very very rude. At the same time, it also sounds so funny that she calls him -씨.
If it is difficult to find how to call someone, we usually talk to them without calling their name and title. I really don't have a clue why he was upset when he was called 오빠.
Please don't be misled about Korean usage by one odd Korean guy.