The problem in a nutshell. Europe eventually came into its own in no small part because there was very limited centralization of power. While they started way behind the curve, outside technologies really fueled and bootstrapped what was otherwise a (relatively) highly competitive free market system with a mediocre educational basis. Europe was never amenable to centralization and this made it very competitive. For a while, the Catholic church came close to making Europe share the fate of China, but it slipped through their fingers as well. China was very advanced, but the environment wasn't competitive which dampened progress. Europe was backward but also highly competitive and adaptive, and only needed to be primed with someone else's technologies.
The Europeans had difficulty developing the core technologies, but the social, political, and cultural climate allowed them to exploit the core technologies developed by other peoples despite their initial barbarian status, allowing them to bootstrap to the same level as other cultures rather quickly.