It seems odd to me that if they are truly only friends that he would have a problem with you meeting her. Frankly, a good guy with nothing to hide would WANT you to meet his friends and welcome the opportunity to demonstrate that he not only cares about you and your feelings, but that he wants you to feel secure.
On the other hand, if someone is going to cheat you cannot build a wall tall enough to keep them in.
I don’t know how old you are, how serious your relationship is with this guy or where you want it to go, but in my opinion, if you and he are in a mutually exclusive relationship he needs to either introduce you to this “friend” or you need to be prepared to walk away… unless you are willing to live with the feeling of insecurity, doubt and (potential) betrayal.
Personally, I would not want to be with someone that I felt I couldn’t trust.
My advice to you is to listen to your intution… There is a little voice inside you telling saying “something isn’t right”. You need to listen to it.
