Should I continue to pursue this relationship or just leave it?

Me and this girl, let's call her Nancy, started talking a few months ago and we really hit it off in the beginning. We go to university together and often have the same classes, so we would go out for lunch almost after every class and even plan trips on the weekends. We live kind of far from each other, about an hour, but we would still plan to visit each other. She was the one that started it by making an excuse to come out to me so that we could study together, but we didn't do any studying and just spent time with each other. However, recently I've been noticing some behavior that I don't really like, for instance, she will take phone calls or text while were together, but I didn't really make it a big deal because I know she has the responsibility of taking care of her family and for some family members she doesn't get to see, so I let it go. It's not that she's on her phone all the time, most of time we are giving each other undivided attention. But we got into a conversation a few weeks ago and she said something that really bothered me. We were talking about compromises in a relationship, I told her that in a relationship I wouldn't feel comfortable with my girl going to a bar or club by herself or with friends that I don't trust, not saying I want to control her life, but I want her to understand that she is putting herself in a precarious situation because there are true predator's out there that take advantage of those moments, but a compromise I would make is that if she assured me by telling me who she was going with and if they were friends that I also trusted as well as her keeping me updated then I would be okay with it despite felling uncomfortable. She then went on to say that she wouldn't care and would go anyways, but what this meant to me was that she wouldn't care about my boundaries. She went on to tell me that if the guy was doing something she wasn't comfortable with then she would expect him to give it up. Now, I'm having second thoughts.

Updates
+1 y
I am not asking her to give up on her lifestyle, but I am concerned about her safety because I care. I'm just saying that I would want her to go with friends rather than go by herself because there are real dangers, what if someone finds her drunk and inebriated and takes advantage of her? I'm not concerned with her cheating. But to reiterate, she told me that she would expect me to give up parts of my life that she was uncomfortable with, but she won't even consider altering parts of her life.
Updates
+1 y
You can call me possessive, but I never once said she had to do what I tell her to do. I just want her to consider my concerns.
Should I continue to pursue this relationship or just leave it?
Post Opinion