Why would you avoid looking at someone?

qstoffe
If you see someone looking at you in your peripheral vision, what would stop you from turning your head and look back at that person?

I was looking at a girl I like. I've only said hi to her a few times. I was looking at her from a distance of around 6 yards. I looked at her for about 5 seconds or so. During this time I could see that she was looking back at me from the corner of her eyes but she wouldn't turn her head to face me. She has done this one time before this.

It's not like she never looks at me, I just wonder why she sometimes only looks back from the corner of her eyes.
Why would you avoid looking at someone?
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