Great posts here! Bud has explained this far more articulately than I ever could and Cookie accurately describes some of the issues arising from using edging and edge pressure as the dominant turning mechanism in beginner turns.
I want to add a bit to the subject of teaching leg rotation to beginners. Even though this is difficult for them and often an unfamiliar task I have found it possible to link this skill to existing skills. Shortly after introducing my students to their skis and teaching them to put them on I have often had them begin walking on the skis. After a bit of that I have had them "walk" by sliding the skis rather than picking them up and putting them down which (sliding) is demonstrably easier and less fatiguing. On the flats which we were fortunate to have at the bottom of the teaching area I had them follow me, sliding their feet alternately forward as I lead them in circles. This was a perfect opportunity to instill the importance of correct fore and aft weight distribution. Most of the time if a skier has a difficult time actively turning their skis it is because they are either too forward (seldom) or back (the usual case). I would get them to follow me in these circles by keeping their skis on the snow, not allowing them to pick them up and demonstrate the importance of keeping the feet back beneath the body. Accomplishing this task requires the use of leg rotation and it is an opportunity to instill the recognition of a fundamental rule that "most of the time, if you cannot turn your skis you are in the backseat" (I didn't actually use this term though) and the remedy is simply to pull your feet back beneath you to crrect your position. They can begin to learn this before they have even ventured onto inclined terrain and thus have begun developing both effective fore and aft balancing and leg rotation before being faced with the need to make a turn. The goal is not to have them pulling their feet back in forth in their skiing obviously but to teach leg rotation and and an effective stance.
I don't know how commonly this teaching sequence is used but, as a general rule, I found it useful to provide the opportunity, if possible, to develop an essential skill before being placed in a threatening (ie perceived as hazardous) situation in which the skill is called for. Use of this sequence helped to provide the students with the necessary skills to turn their skis into a wedge and to make a wedge turn before they were sliding down the hill.
If I may offer a humble suggestion: Understanding what you are doing as you teach and exactly why you are doing what you are doing and the significance of when you introduce certain things is really critical to being able to respond to your students needs and re-fashion your approach in response to them. Even though I may have described a typical approach I have used the fact is that no two classes, no two days, no two snow conditions, no two lessons taught are ever, nor should they be, exactly alike. The greatest task for a teacher is to be persistently observant and perpetually creative in order to teach effectively.