A horse perceives eye contact as provocative, as if it and its status in the herd are not being respected. If it cannot avoid eye contact, it will react in a different way, by rebelling for example. In dressage you don't get anywhere by not showing respect, however superior your species might be. Any animal trainer can tell you that. In the mountains in Argentina there's a wild horse which will jump off the nearest precipice if any human tries to ride it.
