Answer:

Keeping your body facing down the falline produces a strong state of counter at the end of your turns.  It’s a rotational state called “Anticipation”, and it’s like coiling a spring in your abdomen. The moment  you release the turn, that spring is released, and your skis try to auto-pivot back downhill to join the direction your body is pointing. Putting it more simply facing downhill makes the skis tend to pivot.

You need to learn to make all sorts of turns not just ones with a pivot.

See the problem?  It encourages a pivot.  A pivot is not necessarily a bad thing to do.  Sometimes, on steep and narrow slopes it comes in handy.  Also in moguls.  But it’s not what you want to do all the time.  For the learning skier who still has a default pivot built into all their turns, keeping your body facing down the falline makes it nearly impossible to eliminate that pivot.  As long as they try to stick to that “body faces downhill” advice, they will be forever stuck in there pivoting habit.

Facing the same direction as the skis makes learning a clean steered or carved turn easier. Keeping your body more square to your skis as you steer eliminates that torqued spring effect, and therefore makes learning to execute non-pivoted turn initiations much easier.  Once you get your turn initiations free of pivots, slight amounts of counter can be added to help with edging, or heavy counter can be utilized to create an anticipated state when executing a pivot is actually needed or desired.

Learn to pivot after you have learnt clean turn initiations. Save facing downhill for these more advanced skills.