I have always thought that not looking people in the eyes has more to it than insecurity. Yes, insecurity is one very valid as well as common reason. But, it could be more than that.
I am very empathic - psychically so. One of the ways I can 'feel' another's wholeness is to gaze into their eyes. It leads me directly to the soul. I can discern emotions of the other and all sorts of energies. Now, I know this is not a board for this type of converstation, however, I mention it here in order to make a point that there are other reasons not to look into eyes. Ask yourself, when you look into someone's eyes, do you seem to get overwhelmed with emotions which may appear suddenly? If so, then it could be that you are empathically picking up the emotions of the other. Some people can do this and not know they are doing it. I have found it very common in people with long term abuse. We have learned without realizing it that we can 'read' the emotional level of the abuser before he/she has walked into the door.
Lovers look into each others eyes and feel each other at a heart level. This is a positive example of an emotional transference.
Now, filter a possibility that the eye gazer may not be able to know themselves from a deep level. This being the case, then yes, insecurity comes to mind. There is a vulnerability at opening ourselves so much when we gaze into the eyes of another. Say, perhaps that no one has ever shared love with you by looking lovingly into your eyes. This would cause an uncomfortable feeling for you when it happens now, for it would be a new experience. Also, filter in the negative possibility: did an abusive parent look right into your eyes while being abusive?
To look into the eyes of another and allow the openeness of energy sharing, I think at least three things must be in place: 1) you have to know your own emotions and be comfortable with them 2) you need the ability to discern the emotional level of another. 3) You are comfortable giving love and receiving love from another person, for one of the strongest ways to convey this level of acceptance is to gaze into someone's eyes.
One more thing...those of us who have hearing difficulties will stare at the mouth of the other people when they are talking in order to help understand the words being said.
Lots of thoughts came to mind...wrote them hurridly. Nice topic.