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On our fifth date, we bumped into a friend of mine and I introduced her as my gf. At this point she gave me a weird look. After the friend left, she asked me when she had become my gf and told me that I needed to chase her. I mean if she wasn't into me, I don't think she would bother spending 4 hours explaining to me why she wanted to leave me. After I told her goodbye, her response was "that's it?".
Alarmbells of fucked-up-ness ringing loud and clear son. At a point I was dating a chick for three weeks including sleep overs and hours of kissing and then she still was confused about whether she considered me as her boyfriend when she also said she was religious, monogamous, etc. Should learn from that; all this moral posturing is not to be trusted.
In your scenario, there is the risk of really developing feelings for that girl, and at that point she has control over you. The relationships in which you really care are never the ones that last. But when she says that she wants you to chase her, it's a code word for "do things for me that are of benefit for me, make me feel desired." Yet at the same time if you do this, you make your availableness obvious, which means to them that you don't have many other options, and therefore you will lower yourself in status. It's a hold where you pretty much cannot win.
Also you try to apply male logic to the female nature. You wouldn't spend four hours talking unless it served a purpose. For her, a purpose is totally irrelevant; the world has males for that. She is just spilling her mind for the heck of it, because why not. To you it sounds absurd, but females have a thing for endless talks about emotions. Especially when they convince themselves that they cant see you as lover, but still think you are adorable and therefore don't want to hurt your feelings.