I think what Red said was on point, however I can see where you would feel like it was a double standard. Ekltc also had a good question. Are her fears due to the fact that she had a bf before you and her were poly? Definitely curious about that fact.
Use this to open up lines of communication and discuss things between the two of you. As many people have said open lines of communication are key to making this lifestyle successful.
Live life to the fullest 'cause you never know if you're gonna wake up tomorrow!