I've always had it, I think, but I've only just recently noticed that it's really not normal. I just hate it, especially with women. Even with people I've known for years and family members, when I'm making eye contact with them, there's always this nagging voice at the back of my head telling me to look away.
Stop looking away.
In Soviet Union, eyes contact YOU.
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Buy The Gathering!
You should always make eye contact:
1) When you toast a drink with someone
2) When you shake someone's hand
3) When saying something important, like a thank you or an apology
If looking someone directly in the eye seems to be a problem, try focusing on the bridge of the nose between the eyebrows of the person in question.
Hope that helps.