I never even noticed I did this until my psycologist pointed it out to me. I'd noticed other traits in myself, which is why I decided to get diagnosed. I'd been seeing her for a while for other reasons, and when I brought up the possibility of AS with her, she instantly said, "I've noticed you don't make eye contact." I thought about it and realized she's right...I could tell you exactly what is on the shelf behind her chair, but not what color her eyes are! After a bit more reflection, I remember how my younger brother would tell me that when I was talking near a reflective surface, I talked to my reflection instead of the person I was conversing with. He's right and he's wrong. I wasn't watching myself, but I was avoiding eye contact.
It does not come naturally to me to look someone in the eye; like Cockney Rebel says, the better I know someone, the easier it is. I can maintain eye contact with my parents, my husband, and my dog, but pretty much no one else. Some people find it offensive, some aren't really bothered by it. However, because it is my natural inclination to look elsewhere than someone's eyes, I find it very distracting and awkward to look someone in the eye. I have a hard time understanding or paying attention to what someone is saying if I watch their eyes; I function better if I watch the other person's mouth. In addition. I've never figured out how long you look someone in the eye, so people will think I'm staring. A high school classmate accused me of "staring" at her in science class. In college, a woman who thought I was always staring at her confronted me about it. In both cases, I had no idea what they were talking about, but I felt really bad! (I still think I was more looking near them, than at them...for example, the girl in high school sat across the room from me; if I studied the shelf over her head, she thought I was staring at her.)
It's possible that if I'd been diagnosed as a child, Cognitive Behavioral Therapy could have helped me develop skills that would make it possible to understand someone while meeting their eyes, and how long to hold someone's eyes without staring. Instead, I grew up with this avoidance as a natural part of me, something I was completely unaware of. Now I know I do it, but it's just too hard to meet someone's eyes and let my brain function fully at the same time!