Remember that most predators in North America have forward looking, close set eyes. instinctively most prey animals get very nervous when stared at. If, as humans, we had eyes set on the sides of our head (like elk, horses, cows, deer, etc) then we would be looked at as no harm. However, a humans forward looking, close set eyes resemble those of a coyote, wolf, bear or bobcat hence the instinct to be afraid, even if a deer has never seen a human. Follow JB's advice, look away or down but not at a deer you want to shoot until you are ready to pull the trigger.