I've wrestled with this question for years. For the entirety of the dark ages, there was little development of armor and weapons. Late in the middle ages, this stasis changed, leading to an arms race that's lasted until today. For a while, I thought that the arms race itself was the explanation, but that doesn't explain why earlier in the middle ages there was no arms race, despite an equally combative culture, nor why other places in the world didn't engage in the same arms race.
If you follow the progression of armor, you see a steady development of various protections. These protections led to changed fighting styles, and the new styles required new protections. It's the fact that there was active development tailored to the battlefield that gives us the clue as to why Europe developed such fantastic armor.
Warriors talked to blacksmiths.
I will make many gross generalizations.
In other parts of the world, for whatever reason, the military classes likely didn't interact with the crafting classes. Internal cultural barriers existed to keep these two classes from interacting.
In Europe, something brought these two classes together so that the needs of one (the warriors) became the development projects of the others (the armor smiths). Once that happened, once improved armors began appearing, the race to develop better armors was on. An iteration cycle began, with every generation improving on the previous generation. That introduced obsolescence, so that the overall need for armor increased, providing more work for armor smiths. Innovation became the engine of profitability. Profitability funded innovation. Eventually innovation led to faster production. A sheet of steel could be shaped faster than mail could be linked, so armor that used more sheeted steel actually wound up requiring less manpower while selling at the same price, which meant more profit.
What could have happened? The Crusades. During those years, the Europeans saw many west Asian armor styles not used in Europe. They would have been foolish to ignore any features that would have improved their own protection or mobility. With a sudden fervor for unique and different armors, armorers responded to the marketplace with imitation armors and armor implementing their own ideas on protection. Different became acceptable. Innovation became a selling point. The knightly class's desire for new and better turned into a culture of new and better. From there, steady innovation took the mail of the dark ages and developed it into the full plate in just a few hundred years.
What I like about this theory is that no special knowledge is needed. Once activated, market forces drive further development. Once development is expected, it becomes demanded.