My girlfriend (ex as of now) [f/19] and I [m/19] just broke up for a BS reason. I feel remorse, but am convinced she wasn't right for me. What do you guys think?

So my girlfriend of 3 months just broke up with me the other day for a pretty bs reason. I'm 19,male; she's 19, female. So I had taken her out to dinner before we went to a movie. During dinner, she said she didn't trust me. I asked her why, and she said she just doesn't trust me with other girls. Now I have NEVER given her a reason to ever think I would be unloyal to her. She said it was because I typed on my facebook an inside joke between a friend of mine from that friend's computer (this 3rd person friend is a girl). The joke was strictly a joke,as well as obviously a joke. My gf snapped and started texting me asking about who she is and that she didn't like that. But anyway, so we walked to the movie, still discussing this, and we walk in to the movie and I said, "Ya know, if you told me not to hang out with a friend of mine, just because they were a girl, I'd still hang out with them. I'm not throwing any of my friendships away just because you don't like the fact they are a girl." She snapped, said I don't care about her feelings, and said we were done. But what's bs is that she only has like 2 friends that are girls...every other friend is a guy, who she hangs with all the time, and I never say anything about it.

So we had just broken up, and I drive her back to her car where she parked it, and we get into a bigger argument. I confess to her about how miserable I was for part of the relationship because of how controlling she was. She broke up with me another time because I said I didn't care about her thoughts or feelings towards me keeping a gun in my house (this was a hypothetical situation on what our futures would be like), I would still do it to have some sort of protection in case somebody broke in; I'd rather just hahe her be pissed at me, then her getting hurt. She took this as "I don't care at all about your feelings", which I assured her was not how I felt, except for this very specific example. Didn't matter-she still broke up with me...I get a phone call an hour later with her sobbing,asking for me back, so I gave her a second chance.

Anyway, that was just one of many examples of how she would lose her head over something I didn't think she needed to. I feel like I was not only in the right during the gun conversation, but as well as the hanging with friends conversation.

I'm convinced that somebody who is that paranoid and overreacting about stuff that really isn't a big deal isn't date-worthy. What do you guys think?

TL;DR: Ex gf broke up with me because I told her I'd hang with my friends that were girls regardless of her feeligns, because I'm not throwing friendships away for her. She snapped, broke up with me, and here I am. She was very controlling in the relationship, and I felt like she only showed me love when I acted like the Mr. Perfect Boyfriend for her. Otherwise she would get upset with me. I hated that I had to be someone I'm not for her. She also got mad at the fact I told her if we were ever together in the future, I would keep a gun in the house to protect the family with, regardless of her thoughts on it. Shes doesn't like guns, and doesn't like the idea of me with one, so she said that was a no-go, it didn't matter if it was to protect the family or not, she wasn't going to have it. Do you guys think she was somebody date-worthy?