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So to summarize your point, it's not wise to ASK questions, but tell her what I feel about certain topics and sort of.. challenge her?
Yupp thats pretty much accurate, challenge her and make her qualify to you.
One of the best qualification examples comes from Mystery and goes something like this:
You: Why are guys attracted to girls?
Her: Because of their looks.
You: I figured you'd say that
Her: Why..?
You: Most people do, but beauty is common. For me, personality and good energy are much more important. Shallow girls are pretty boring.
Remember, you must bring these type of techniques in a light and playful manner, not serious as if you are ready to propose to this poor girl

If you have done it correctly she will start to second guess herself and convey to you how she isnt shallow and she has good energy -> qualify herself to you. Now you have control of the interaction and she is inside your frame.
For the leaving part, either she wasnt in your frame or your frame wasnt strong enough because from how you describe it, it was an interview type of situation or a one way traffic thing.
"You: Most people do, but beauty is common. For me, personality and good energy are much more important. Shallow girls are pretty boring."