<human>: We started seeing each other a few months ago, and we weren't really sure where we wanted to go with it. At the time we agreed to keep it casual.

 We're both in school.  She's a very busy undergraduate, lots of activities and classes.  She receives a lot of attention from other men due to her attractiveness, intelligence, and activity, but vehemently declares herself to be a "Social Cripple" despite her being very easy to talk to and seemingly happy all the time. 

We were out to dinner this evening, with plans for her to come over after her lab is over.  I walk her to her class, and right before she goes inside, she says "Can we talk about something quickly?"  So we do. She stumbles around a bit with her words but basically says "I just want to be friends."  I'm not interested in that kind of arrangement at this time, and I tell her that.  She has to go to class, so I put my hand on her shoulder and say "We can talk more about this later." Meaning after I pick her up from her lab. 

I really like this girl, and I do not want to just be friends with her.  

How can I best approach this conversation?

Can you succinctly summarize the text in 1-3 sentences?
<bot>: A girl I've been hooking up with wants to just be friends, I don't want to just be friends.