Once learned, side-slipping is easy. But there are several things that make learning it quite difficult.
I teach a lot of adult beginner groups, and almost always do a side-slip session with them as I lead them down the beginner hill. We have to get down this one short-ish section that looks steep to them, and it's at the top before they cement their turning skills. I have them side-step down the first part of it because I've had them doing plenty of side-steps beforehand. They are uncertain about the pitch, but they all are able to side-step down it anyway. Then I slowly show them how to smooth the side-steps out into side-slipping. I do this in sections, a little bit at a time.
We are half way down this pitch at this point; to them it looks like miles and miles, so they are motivated to do it the faster way (side-slipping) instead of stepping the whole way down. I climb back up and side-slip down beside them, one by one (tiring!) After everyone tries the side-slipping, I give them the option to keep using side-steps if they choose. We eventually make our way down to where the pitch becomes more shallow. It takes a bit of time.
Most can't do the side-slipping, some can, and in their short lesson with me they usually don't get a second try because time runs out. I used to not understand why so many had so much trouble with the slipping. I figured it was the fear. Fear (there is no flat run-out, so they all feel fear) makes them want to look and lean uphill; we work on that. But there's something else going on, and I think I've discovered what it is.
About four years ago I had trouble with boots that I had just bought (from a respected boot-fitter, by the way). Those boots gave me all kinds of pain, sometimes sending me away from the mountain in the middle of the day in an emergency boot-fitter visit. Towards the end of the season my liners packed out dramatically, all-of-a-sudden (or maybe my feet shrank, or both), and I started to sense way too much room in the boot width-wise and volume-wise. I decided to buy new boots the following fall when new stock appeared in the shops.
One day, when I was side-slipping my beginner group down that pitch, I felt insecure in my side-slips. No, I felt fear. Those boots allowed my feet to slip sideways inside them, which severely reduced my control over each ski's angle to the snow. I was an instructor feeling fear on a little side-slip on the bunny hill, and that fear was coming from my boots not fitting right. And that fear was justified; it reflected actual lack of control with no way to regain it short of going shopping.
I realized my students must be experiencing this same thing in their rental boots -- which were probably too wide, probably too tall in volume, too loose around the ankle and lower leg. All of these lead to little control over edge-angles, as well as the direction the skis are pointed.
They probably think it's them. They think it's their courage or their lack of skill. That's sad. The only real fix is a boot that does not allow sideways slippage of their feet, and as I've discovered the hard way that can be a multi-year search for the right boot fitter.
By the way, I'm in the right boots now, with all the right modifications, due to me finally finding the right guy who took my feet seriously.