You need to talk to him. After all, he's your friend, as well as girl is.
You have to explain him that just because she's a girl doesn't mean you are trying to steal her. Ask him how would he react if it was a guy you are befriend with. There shouldn't be limits on gender, and just because man is talking to a girl doesn't mean he wants her for himself.
You won't solve anything by playing hot potato. Tell him you don't like his current behavior, and that he should just stop acting as if you are trying to steal his girl. He's senior and yet, he acts like a kindergarten child. I do understand he is just afraid of losing anyone, but if he chose girl instead of you, that's not right. Currently, he is annoyed by everything. Don't try ignoring him, he'll get even more angry if you ignore him.
As I said, you need to talk seriosly and tell him that is a normal relationship between two friends. Not everything needs to grow in romantic relationship just because one's guy and other's a girl. It's a brother-sister relationship and not R from romance can grow from such a relationship, and yet, it's much better having girl feeling a sister-brother relationship towards you than romantic feelings. Explain that he is your friend and should gain more trust in you.
Of course, be sure to tell him the truth and don't betray your friend. Arguing because of a girl is silly and leads to blank arguments.