Helluva an Jamt, great comments!
I'll just add a couple points... hi-C does not necessarily mean no skidding. It means the ski is engaged, bent and steering the skier on a round turn path, starting as high as possible. That could be arcing, or it could be brushed a bit for speed control. The way to distinguish the difference between a nicely brushed hi-C and say a pivoty skiddy thing, is whether the tail is progressively fanning out, or if the skis are drastically pivoting such that they are changing the direction they are pointing faster then they are redirecting the skier on a curved path. Those things flag lack of edge engagement and lack of hi-C turn shape. If the uphill ski stems, that's also a sign of lost high-C.
Helluva is absolutely right about avoiding "pushing" movements to create pressure, but pressure development is necessary, its a question of how. Do it wrong and you'll screw up hi-C. Ski into the pressure, rather than trying to push with your feet. Getting "upside down" means someone skiing behind you could see the bottoms of your skis before you get to the fall line.
If you are going slow, you will have to actively angulate more and sooner in order to stay in balance, otherwise you will probably fall down the hill as you show the bases of your skis to the guys behind you. As you pick up more speed, you can delay angulation a bit, you can create turn forces by getting your skis to bend, and ski into that bend, to create those pressure forces that will get you upside down and not falling down. Its very good practice to see if you can get upside down at slow speed. Many great comments here about developing a finesse for progressively developing edge angles, even at big speed. A bit of early angulation helps to do that better if you are trying to get upside down. This provides a way to ski forward into the bent ski, rather than falling down the hill and hoping the ski will bend and catch up to you sometime before the apex. If you are progressively developing edge angles, then the ski also bends progressively, so a bit of early angulation will enable you to be in high-c, with engagement, upside down...but progressively.
It is possible to get a little bit upside down with an extension move, as endorsed by many, particularly at speed. However, you can really get a lot more upside down, as Helluva pointed out, by flexing to release the downhill leg and tipping it like crazy to develop edge angles and ski into the pressure. When you extend yourself down the hill, you do move your CoM down the hill and you do get an initial bit of pressure, but then once you've used up your range of motion, you will lose pressure. So there is much more of a performance limit there in terms of radical upside downedness. Conversely, flexing to release the downhill leg moves your CoM across without having to push yourself there. Skiing forward into the pressure rather than pushing your leg to get it, creates a more sustainable pressure state as you develop hi-C turn shape.
Flexing to release is also generally more conducive to early angulation, as Helluva pointed out, which at slower speeds is crucial for getting upside down high-C turn shape.