I could not grasp the probability maths (still shit at it, sorry Ms Von Savant) but I could write a program to experimentally demonstrate it, so I did.
In QBasic. Because that's what we had and we were happy.
The way the problem works started coming together in my head as I coded it. The code’s structure reflected the problem’s structure. I realized I previously misunderstood something about the problem statement. Later, I read someone saying many mathematicians got this problem wrong because of how it’s worded.
So, it may be challenging, not because probability was challenging, but because it was unclearly specified. That’s the cause of many software errors, too.
People who get it wrong are usually projecting some implied understanding onto it, which is why they get it wrong.
Which is the point of the problem. It's designed to reveal this tendency in analytical thinking leading to unexpected outcomes. You get it wrong, you're gobsmacked, you understand why, you gain some enlightenment from it. It's fun to be wrong in ways you later understand. (This is one of the thrills of programming: that moment during debugging when you shriek with joy: "YES, IT BROKE!")
The fact that it also exposes the way some overly confident people lash out with anger that exposes other biases is the point of the article, I think.
It was years before I understood the actual lesson here -- both the probability lesson and also the way it hints at the fundamental truth that in life, binary choices may have been weighted in ways you don't understand, perhaps by the people asking you to make the choice.