Eye contact is a big deal, it signifies everything already pointed out on this thread and more, it is the first thing people use to find out things, simply from how engaging you are to how your mood is, that said, i find it awkward.
As a person who regularly does presentations for things in college classes, i find it EXTREMELY unnerving when people in the audience try and hold your eye contact, for whatever reason they have, it instantly makes me feel flustered and clumsy, I'm a person who will avoid extended eye contact and instead use my body language to accentuate whatever it is the person needs to know, you could i'm one of those people who use hand motions when speaking, simply to help get my point across in exchange of eye contact,
That said, my main reason for avoiding eye contact is again what Neko and others have said, Giving the idea that you like someone, I have noticed that when around someone i am interested in i get the most basic phase of eye dilation in relation to arousal/stimulation, mostly due to the extra surge of emotions of being around someone i am interested in, and i do my best to avoid eye contact as it is incredibly easy to notice when my eyes are like this due to the lenses of my glasses making my eyes appear bigger.
TL:DR, Eye contact is a tricky system, I avoid it like many of yourselves for a myriad of reasons from belying feelings to plain silly things like thinking my eyes are unnatractive because of their color.