Why do some girls get awkward and resistant when they find out a guy she likes likes her back?

Here's an example: I was doing job training and when I transferred, there was a going away party. Everyone went except for one girl, a girl whom I really wanted to go. Her friends told me that she confessed she liked me and was really sad I was being transferred, and they urged me to talk to her. So I tracked her down and told her I really wanted her to go and I wanted to spend some time with her. She was too busy and was committed to not going to my going away party. I found her my last day and again, she was very resistant and said very little. After I moved to a different state, people would call me and hand her the phone, but it was kinda late.

I've seen stuff like that happen more than once: a girl will convey interest but become very resistant and awkward when they find I like them back. It seems kind of backwards and I would assume a girl would be thrilled and become confident. Why might a girl become nervous and evasive when they're into me and find out I like them? (It doesn't seem as simple as "you got the wrong idea", because the girls have told their friends she liked me.)
Why do some girls get awkward and resistant when they find out a guy she likes likes her back?
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