Most Helpful Guy
A common problem you have.
The problem lies with her, not you. She has either been cheated on before, or the men in her life (father, male family members, male friends) have abandoned her at some point and she thinks all men are untrustworthy.
Your best course of action is to get rid of her. Simply put, she will NEVER trust you, nor any other boyfriend in her life. Maintaining a relationship with her essentially means you must cut out every other woman in your life. She will ensure that every current and new friend that is female will be deleted from your phone and facebook.
There's very little you can do about this behavior from her, because it has probably been ongoing for years and it is a part of her personality now.
Besides, it's better that you find someone who trusts you. Even if a girl thinks you are untrustworthy - at least she should have a good reason to be. For example, if you're flirting with other girls... etc.
I am one of those people who get along with girls very well. All of my friends are girls (I had trouble selecting a male for my groomsman, so I picked 2 groomswomen). My wife trusts me because she sees how I interact with my female friends and it's not flirty. Sometimes, she even takes my phone and sets up a "date" with the girl friends I have, just to get me out of the house. Then she tells me that, "You have to meet Carmen tomorrow because you haven't talked to her in awhile."
That is trust, and that is what you need more of in your relationship.