I'm not that type of person

My girlfriend and I have been dating for a few months now. She is very inexperienced when it comes to relationships. Over the past few months, we have had our issues just like every other relationship. Just recently we got into a fight about how we communicate with each other in different ways. When we were discussing it, she said that she hates how I act whenever we have a disagreement. She says that whenever we are discussing stuff, I always have this blank stare on my face. She says that this blank stare, to her, means that I have nothing to say to her and that I don’t want to share anything that is going on in my head. She also says that she see’s that same blank stare on my face whenever we are fooling around. So she basically thinks that whenever we arguing, all I want to do is fool around, and I don’t want to participate in talking at all. The way that she discusses things with me is yelling and attacking. I keep my calm. I don’t yell back, and I don’t make any notion that I’m attacking her in any way. This is because I’m smart, and I realize that fighting fire with fire just makes it grow. So I keep my calm. We did, however, resolve the communication problem. And I told her that the blank stare that she see’s on my face is 1) me keeping my calm 2) I can honestly say that I make sure that I think about things before I say it. 3) I listen to everything she has to say. That is why my face is like that. She believes me about 1-3. That miss-communication issue is resolved. However, she is 100% convinced now that all I want in this relationship is sex. I have never had sex before and neither has she. I’ve gone to 3rd with my last girlfriend and she has barley made out with someone. I can see why it may seem like I’m a little bit more encouraging whenever we are fooling around, but I don’t know how to convince her that I do not want to date her for sex or anything like that. She thinks that whenever we fight I’m horny and I want to fool around. How can I convince her otherwise? Because I can honestly say that I don’t. I’ve tried to tell her otherwise, and I’ve tried to explain it. I hate being called the guy who wants to get into a girls pants. That’s not be. I’m (I guess you could call it) very straight edge, and I would never push anyone’s limits. I respect her. But she doesn’t believe me. Can anyone help? (sorry this is so long. I just needed to explain the whole situation)