I think you kind of blew it already. Imagine that the roles were reversed, and that she had actually talked too you in the way you talked to her:
Her: "What is your most attractive quality?"
You: [you mention some quality that you possess]
Her: "Well that's easy to change."
You: "Why should I want to change that?"
Her: "Because that is obviously not attractive. I'm afraid you're too stupid to understand why, but I do understand and I'm telling you it's not good."

Would you be attracted to this girl? Of course not, you would feel insulted by her presumptuousness and her judgmental mentality. And that is precisely how you made her feel. So spend a moment of thought on how the other person will feel when you say something to them before you actually say it.

As for how to continue, you may able to salvage this by changing the subject. An interesting riddle or dilemma would allow for a nice bridge: 'So do you understand this? Blablabla.' But realistically speaking, I would not expect her to react anymore, so my advice would be to chat up other girls as well.