One of the mysterious truths about cycling is that your bike will go right where you look. Often times, this is the reason riders crash -- they look fearfully at the thing they don't want to hit, or the place they don't want to go.
Ask any singletrack mountain biker. When the focus is on the notch between two rocks, the wheels have a much better chance of finding it. When the focus is on the rocks, that's where the rider soon is.
Try it this afternoon. When traffic is clear and you can safely play around, try rolling your wheels over or between fallen leaves or lines or spots on the road. Leaves are fun because they crunch to tell you the result.
For example, focus on the space between two leaves that are six inches apart. Good, no crunch! Now try to go through another pair, but this time shift your eyes to look at one you're trying to miss. Hear that?
It's hard not to look at something dangerous you want to miss. But once you've developed the self-control, you'll be able to put your skinny tires through very narrow places.