From the prospective of a woman:
I had a friend who tried to get me to play Runescape for a long time. He REALLY wanted to be my friend but I was cool just playing games with him and that's it. Finally, one night I made an account and started playing with him. It was really bad because I felt like he was more invested into our friendship than I was. Everytime I logged in he would whisper me wanting to play together. Sometimes when I play I just want to play by myself. I finally told him that I was going to stop playing because I wasn't having fun. After a while things died down and he got a girlfriend. I really think he was wanting something more, but I am married. FYI, my husband didn't like him either.
While cutting you off mid sentence was extremely rude and uncalled for, maybe you are more invested in your friendship than she is. If you really only want to be friends either shrug off the fact that she is rude, talk to her about her rudeness or find new friends.