There is a section of trail on Horse Thief (also known as "Close Your Eyes and Hope for the Best") in Arroyo Hondo, NM that I always point out to people as the place I learned a very important riding lesson. I was riding with the FITaos after-school mountain bike program and had just accidentally ridden off the side of the trail. Sean and Susie, being the brilliant leaders that they are, seized the moment as a valuable teaching opportunity and taught me the following:
Look where want to go not where you're afraid of going
So simple! So elegant! So...hard to do. For some reason, as humans, we like to look at things we want to avoid. I think it's because we like to know what we're up against and want to size up the cliff/drop/cactus/river. Unfortunately, looking where you don't want to go has one of two effects. Either your bike "magically" drifts towards it, or it "magically" drifts in the opposite direction. Now, you know why you don't want the former. You're trying to avoid this thing so drifting towards it is bad. But the reason you don't want to drift away either is that there's probably something on the other side of the trail that you also don't want to hit.
For example, let's say you're riding singletrack that is cut into a sidehill. You decide to look down the hill (where you don't want to go). If you drift toward it, you fall down the hill. If you drift away from it, you hit the upward sloping part of the hill on the other side and either get pushed back to the downward side, or crash. Either way, there's a pretty good chance you're going down the hill!
By looking where you want to go your bike tends to go there. It also helps to keep you focused on what you're doing instead of worrying about what could happen if you "ended up over there in that Cholla Cactus. Wow, that would hurt. I wonder if I'd have to go to the ER. Would they use duct tape to pull the spines out or do they have little tweezers for that? And isn't that the plant they make tequila out of? No, wait, that's the Agave plant. What's an Agave? Not a cac...Wait! I'm racing! Focus!"
Plus, what a great life lesson. Focus on what want to do and where want to go instead of getting caught up and distracted by everything that could go wrong. Sounds like a good plan to me.