Okay, let me take one more shot at this: Some data, which illustrates the "Problem" we face as instructors:
"Inflight loss of control is the leading cause of fatalities in aviation. It dominates among homebuilts, in general aviation as a whole, and in the commercial jet fleet worldwide.For the period 2001–2010, the GA JSC found that more fatal general aviation accidents resulted from LOC-I than from the next five occurrence categories combined. One-in-four fatal LOC-I accidents occurred during the maneuvering phase of flight—more than during any other phase. (If separated into its own broad occurrence category, LOC-I while maneuvering would rank third overall, behind CFIT.)."
Here's a chart:

And, here's a breakdown of that statistic:

"
"During safety programs over the last couple of years, nearly 900 pilots were asked, “What is the primary control surface you use when turning an airplane?”
The answers: Elevator, 14 percent
Rudder, 23 percent
Ailerons, 63 percent
Eighty-six percent did not recognize “elevator” as the correct answer. Nearly 1-in-4 believed the rudder turned the airplane despite multiple warnings to the contrary in the FAA’s Airplane Flying Handbook. Even while in an established turn, trainees often fail to identify the elevator as the control being used at that moment to curve the flight path. Hence Langewiesche’s conclusion,“pilots, as a group, simply don’t know how to turn.”
The above Quotes and charts are from Stowell and Winburn 2016, "LEARN TO TURN Reducing Loss of Control through an Improved Training Methodology" excerpted from S.A.F.E. Resource Center, SafePilots.org.
So, Rob, my point is simply that when starting the process of teaching flight in the mountains with a "Pilot", the CFI would be wise to understand what those charts represent.....a singularly poor job historically of our flight training programs of teaching pilots to turn SAFELY. The old flight instructor mantra "Begin Where the Student is At" applies here....big time.
First, we need to ensure that the "student" is actually competent to fly the airplane safely in maneuvering flight.....any CFI will verify that an occasional student will try to kill you, after all, and oftentimes, those are pretty "experienced" pilots. Or at least that's what their logbooks might suggest.
Now, getting into the mountains, I can tell you that one of the most difficult tasks for the CFI is to get a "student" to fly close to a canyon wall. This enables us to use the maximum width of the canyon, after all. Seriously, with some folks, you almost need a firearm to get them within 200 feet of dirt or rock--laterally, that is. Oh, they'll often be happy to fly along pretending they're an ag operator, flying at ten feet ABOVE dirt/rock. But, just try to get them to move to one side of a canyon.
Then, of course, there's actually understanding and predicting the direction, velocity and resultant EFFECT of any wind. That is a book unto itself, but needs to be well understood so as to decide a) What side of a canyon to fly, and, more importantly b) Whether we even want to be IN that canyon today.
Once turning is mastered (and believe me, I've run into a number of experienced pilots who weren't very competent at that basic skill), we understand the effects of winds in terrain, the notion of density altitude, etc, etc.....we MAY be ready to operate safely in mountainous terrain. Maybe.
Rob has noted that you have to be pretty HUA (Head Up A...) to actually paint yourself into a canyon that you can't turn around in.....and I certainly wouldn't argue that. Nevertheless, it happens, unfortunately it happens somewhat regularly.
So, really, what I've been talking about in this thread is that the pilot really needs to know how to fly his/her airplane, and turning is obviously, based on the charts above, something many pilots don't do well.
And then, of course, that pilot also needs to know a good bit about mountain weather, effects of wind, etc. to safely operate in mountainous terrain. But, that's beyond the scope of this discussion.
Most of all, learn to turn....safely.
MTV