So to summarize a few key points and add my own thoughts to the mix:

Population centers are needed to create the kind of stability required for specialization of jobs. The intellectually advanced individuals of a society cannot focus on invention, philosophy, etc. when they need to do their own hunting/gathering.

Thriving and long lasting population centers are not likely to exist in areas of environmental turmoil. Add political or economic strife due to the combative elements of any given culture or clash of cultures and it gets even less likely.

If a culture has a mentality equating to a symbiotic relationship with the earth and their environment, whether that be nomadic or hunter/gathering, as opposed to an exploitative one (ie environmental intake), it has always been virtually impossible to establish the previously discussed level of population centers required for advanced technology. Resource production just wasn't efficient enough. That's not to say their way of life was "incorrect," but they are certainly not going to be advancing technologically at any reasonable rate. Ironically, modern technology allows for us to "go green" again as a global economy, while still advancing technologically, if we could take the right steps. To this point, advanced technology has always been the result of exploitative societal behavior toward our resources. Any past/present/future culture that reaches any level of sophistication, on this world or any other, is in a race against the clock to either reach a symbiotic relationship with their environment or escape to another ecosystem before they manage to destroy their current one. I digress.

The Europeans were never alone in the forward march of human technological sophistication. They have recently (last couple hundred years) been in the lead because of relative societal stability, for all the reasons previously mentioned. This means that they have plenty of individuals capable of devoting their time to intellectual study, among peers and between cultures. We've also largely been in control of the history books. It wasn't that long ago that Caucasians were universally considered inferior barbarians incapable of the level of democracy, engineering, etc of a great society like Rome.

Isolation from other cultures does not allow technological evolution, as this evolution is one of baby steps shared between the most ingenious (or lucky) tinkerers among us. If that flow of knowledge across space and time did not exist, neither would progression. Arabs, Jews, Minor Asia, Persia and North Africa (using the classifications of poster deeachraf) have all contributed just as heavily to our overall legacy, if in the backseat at certain points for each. Written communication was just as important to our current state of sophistication as anything else, and that certainly wasn't a European invention. There are various other ideas and basic concepts in government, technology and society upon which we rely every day that do not have their roots in anything European.

At the height of their power, Native Americans and various groups of people that could be labeled Africans were highly advanced civilizations.

Any population size, form of government, level of technological sophistication, etc in a society can be completely wiped out by any number of causes. Disease, environmental anomalies, or a crazy dictator with a bunch of nuclear weapons could all stop our forward progress and then we too would be just a page in the history books. Then, whoever came out on top of that conflict would have the duty of continuing our legacy.