Feeling betrayed makes it seem like the female in question is just a mere slave to the affection of men. She chose to be in a relationship with you. The only reason that would make it justified for him to feel betrayed by you would be if she actually liked him, and you lied about him and was like "lolll he has a 2 inch penis" etc etc. Maybe he displays feeling betrayed to masquerade his jealousy. If he was in your situation, I sure as hell doubt he'd care. It's like when one's mother doesn't buy them a candy bar at the supermarket when they're a small child at like 8yrs old, and they cry and go "this isn't fairrrrrr."
If you're not in a serious relationship with her yet, tell him that it's not a serious relationship, and there's nothing stopping him from making a move on her but his own emotions. If you are in a serious relationship with her, then tell her that your friend is angry and feels jealous, and that she should talk to him about it and tell him her feelings for you.