<human>: As the title suggests, whilst discussing where our relationship could go in the context of my girlfriend studying abroad for a year I brought up the possibility of opening up the relationship for that period of time. She's going to be studying an 8 hour time difference and 10 hour flight away so we would see each other a handful of times at most during this period.

Initially she was receptive and said that although undesirable it may be a realistic option. There are still 4 months before she leaves so we decided to chew it over for a while. 

Two weeks later she has come back to me about it. She says that she trusted me and that upon reflection my suggestion constitutes an unforgivable betrayal of that trust. She says that because of this we should just be friends. 

I'm confused. During the original conversation I made it very clear that this was something we both had to be very sure that we wanted and that if she didn't agree then I still want to try and make it work. We have both (I can only account for myself but I trust her) been completely faithful during the course of our relationship and trust has never been an issue for us. Although her reaction and emphasis on trust leads me to believe that it may have been for her.

I like her very much. I want to save this relationship. What can I do?

Can you provide a brief rundown of the text in within 3 sentences?
<bot>: Girlfriend calls my suggestion of an open relationship during a year of long distance a betrayal of her trust and breaks up with me. What can I do?