"Rushing the turn" can mean many things, but it usually involves some sort of excessive pivoting of the skis in the top part of the turn--either as an intentional movement in itself, or (often) as an effect--a necessary correction to get your skis back under you after over-inclining (moving too far inside too quickly) or trying to "pressure" the skis too early by rapidly extending the legs too soon, before the forces of the turn allow you to sustain the pressure.
Rapid leg extension is what you would do to, for example, jump up in the air--it results in a quick increase in pressure, followed by a quick decrease in pressure. If you incline into a turn and then try to "pressure" too soon with that rapid leg extension, you will literally push yourself downhill, away from your skis, which would result in a fall if you didn't then quickly pivot your skis to get them back under you. That's a common error, actually, in many skiers who try to "carve" "as early as possible," lacking the patience we're talking about.
"Rushing the turn" can also simply result from defensive intent--an unwillingness to let the skis and your body move down the hill and gain speed in the top half of the turn--an attempt to avoid the "fall line" and get quickly to the end of the turn. Ironically, in this case, it will be accompanied not by inclining too much too quickly and losing pressure, but by just the opposite: not inclining down the hill enough, or at all, requiring the skis to pivot and brake to avoid running down the hill without you.
Interesting take on "rushing the turn", Bob.
I was thinking just the opposite. We "rush" the turn because we did not get our CoM moving down the hill fast enough coming out of the old turn. We didn't direct the medicine ball down the hill far enough into the next turn when we let it go coming out of the old turn. So at the transition point, we have to do something to get our CoM into the turn more. Twist our skis so we have something to push against sooner or extend our leg to push us downhill sooner, step/stem, something. So I was thinking it is because of under inclining versus over inclining. We delayed letting go of the old turn and had to "rush" into the beginning of the new turn.