As much as it pains to me say this, I was exactly like your girlfriend. I hated my boyfriend talking/hanging out or even looking at other girls. I was jealous, 99% of girls are insecure about themselves, and the other 1% of girls are lying. I didn't believe that he'd cheat on me with these girls, but I was paranoid that maybe he'd think they were better looking than me or they had better qualities than me. It sucks, but there's that much crap going on in the world with guys and girls cheating on their partners that it's hard to get that idea of your head. It's not her fault really, if you think about it. Many many people cheat on their partners, so it's very possible that she's scared you'll do the same. & it doesn't matter how many times you tell each other that it isn't going to happen, she'll still think it at the back of her mind. She can trust you 100% but she'll still get paranoid & doubt you, it's just the way life is. Not only that, she's a girl herself so she knows how other women think. She's going a bit OTT with it, but you have to understand that it's this generation. Not her. Maybe ask her to meet your friends? & then arrange for them all to meet without you around. So she can get to know your friends better, see what they're like without you around.
I did this, and honestly I'm so much better off. I thought this one girl (his old best friend) was gorgeous, x100 better than me, she was learning to drive, she was popular, she went out loads, ect but then after spending some time with her, I realized she wasn't that pretty at all, in actual fact she looked about 14! She was very immature, and had no feelings towards my boyfriend whatsoever. If she starts slagging them off to you, don't take it too seriously. This will just be her way of making herself feel better. Girls for ya, complicated.