It sounds to me that you have agreed to be in a monogamous relationship with her. Have you talked about possibly opening things up in the future? I'm wondering if this might be where her insecurities lie. If she always has in the back of her head that the next person that you're attracted to will be the one that brings about the opening up of the relationship and the end of the type of relationship that she is comfortable with then it's always going to look like a threat.
If I were you I would be very honest with her either saying that you intend to stay monogamous with her for as long as your relationship lasts or that poly is a part of who you are and that you intend to pursue it. It may be that the latter leads to the end of the relationship but if poly is a deal breaker for her and something that you are then by not owning up to it you're just delaying the inevitable.
Also have a talk about her insecurities and where they come from and what might reassure her. Sometimes the demons from our past pop up. Her lack of trust may very well come from something else. She might not even be aware of what that something else is. Poly is a lot of work emotionally. Every little insecurity from your past is brought up and has to be faced. It's not an easy road.
Everything will be ok in the end. If it's not ok it's not the end.