The masters of every subject say stuff like this, and it's really just a type of myopia of the craftsman. I work in manufacturing and people tell you shit like this all the time.

Imagine a 19th Century Car Driver:

"People who think learning to drive should be relatively easy are missing the mastery required for match-rev shifts, air-fuel mixture, spark management - not to mention the intricacies of debugging your carburetor on the side of the road."

Programming will continue to be made more accessible, as is the apparent trend. Nearly no developers know what's really going on under the hood except people who specialize in assembly, CMOS, etc.

Of course it will become easier over time...just like everything. Consider John Carmack and what he did when writing Doom, Wolfenstein, etc...I can almost guarantee you when he was programming, programming was A LOT harder than what it is today. But the difference there is nothing more than time. Even if it's getting easier over time, my main point still stands.

Sure, a simple ray-caster isn't going to need a lot of optimization today. But when you are dealing with the sort of data that is now common. Optimization can be just as important.

While languages have have improved for the better, other things have created other challenges. Consider the PS3 Cell architecture. Considered to be a much more difficult architecture to program for than the processors of Doom's day.

I don't like that advice at all. Sure, not everything's easy, but the hard way is almost certainly not the right way. When I was learning to program (still am, as should all of us who are programmers), pointers came easy, arrays came easy, hash maps came easy. Almost every concept makes sense. I'm not some intellectual godsend either, so I know there are probably a countless amount of others who feel the same way.

I think that the most likely option is that the "teacher," or at least method of teaching, is bad.

Indeed: Hard exercises have an important purpose. They are about problem solving. But so do easy exercises. They force you to make sure you understand the basics of what you're doing, and suss out bad habits before they become ingrained.