It's actually the tail of your downhill ski that falls away. This is a common bad habit that even some accomplished skiers never break. It's called a downstem, and it happens because you're too eager to transfer weight from your downhill ski to your uphill one. You shove the downhill tail away from you to find an edge, and then bounce your weight off that edge toward your uphill ski. This happens because your hip is nudging out (away from the hill) and twisting forward. Get rid of this tendency by keeping your hips square to your skis or even by holding that outside hip back slightly. This hip delay is called countering. Open your stance slightly, think about edging both skis early, and slo-o-owly draw the weight transfer out. Not only will your downstem go away, your skis will stay parallel, and you'll be much smoother.
Instruction Question: Controlling Your Downhill Ski