[Flavalicious]

I personally think you don't communicate your feelings well enough for her to understand why you don't want to hang out with her. Both of you confessed that you love each other but in the other hand you told her that you didn't want to hang out even if it meant missing out on her -- it's the total contrary of how people who love each other would act; Maybe she took it as "you're okay without me around you"; she got hurt and thought that you don't love her anymore. It could be this or other things, we wouldn't know until you find out.

I understand that you don't want her to befriend a guy who hurt your sister, but I'm not sure that she understood. Did you try to tell and explain to her about what happened between your sister and that guy? If she loves you enough, I think she would understand how you feel about him.

If both of you really love each other before this, then I think it's just the matter of miscommunication. And before you even start afresh your relationship with her, you want to fix the thing that made her broke up with you in the first place. Talk to her and find out the reasons she wanted to break up with you and fix it. Then you can ask her whether she would want to have a relationship again with you. Good luck!