I don't know what I should do?

I'm a 23 year old college student and I've been dating a girl of the same age for the past two months but we recently broke up about three weeks ago. However something seems off. We didn't go fast in our relationship and only went so far as to cuddle while watching movies. It was a nice and open relationship where I never felt like I had to hide something or she was hiding something from me. She even told me how happy she was that the relationship was so open minded. However about three weeks ago everything changed. Her parents came down to visit us at our college and take us out around town. I made sure to be respectfull to the parents and try not to pull focus of conversations to me. However the day after they left she suddenly wanted to break up with me. I found this kinda odd and after a bit of questioning came to realize her parents thought we weren't "compatible" though they never said why. They also said they saw red flags in the relationship such as "wanting to sit next to her at dinner when her parents are in town". by the way the parents never told me anything. Even though I was reluctant to break up I ended up agreeing to break up so she could think things over. We remained good friends and she went to Europe for a week. She came back last week and now decided that "we could no longer be friends because I still like you". Im still confused. She also said we werent compatible. I asked why and she couldn't give me any examples. To be honest something felt off. She is usually happy go lucky, even when things are down. But during that last conversation she didn't seem to have any ounce of happiness in her. I don't know what to do.
Should I continue to pursue her? Do you think her parents are trying to make sure she doesn't go out with me for some reason?
I don't know what I should do?
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