Riding in the drops, though it may feel scary at first, is more stable and gives you more control than riding on the hoods.

You want to be in your drops for fast descents, fast corners and for sprinting, as all of these activities can be hazardous on your tops. Mind you we're talking fast here, simply standing to start at a red light on your tops isn't going to toss your off your bike - really reefing on the pedals with your hands on the tops OTOH, can cause you to lose control. Like wise with corners - just going around a corner, no problem, pedaling through a fast corner - get in your drops. Descents - I do suggest that everyone learn to at least use drops for descending, it's just safer to get down in those drops.