I think Otavio summarized the problems of a global historical narrative quite well, although I have a more cynical viewpoint on it.
All history is fundamentally local. They are, after all, records of things that happened in a place by certain people. Attempting a global history requires abstraction and generally results in a more shallow coverage. These abstractions are often controversial and with good reason. For example, trying to fit history into a globalization perspective runs into the great controversy over whether globalization is a modern phenomenon, enabled by modern high-speed transport and communication, or whether globalization is as old as civilization. This is not a question that can really be answered, due to a lack of historical evidence.
There are a lot of reasons to think developments in Europe had a significant and near-immediate effect on developments in East Asia and vice versa since at least the bronze age, but these were not directly recorded, perhaps because they are merely coincidences, perhaps because it happened through series of middlemen\merchants. Many simply pre-date the written record and have to be inferred from archaeological evidence. Global climate trends are also a possible culprit behind some of the apparent co-developments. Records on the volume and types of historical trade are especially lacking until the early modern period, when governments for the first time took an active permanent interest in trade policies.
I think it useful to learn history through the perspectives of the people who lived it. This comes with cultural biases, but that's a good thing. People should learn not just what ancient foreigners did, but why they did it and how they thought about the issues. Just as we should learn how our contemporaries from different places and cultures think differently. It is more important to understand the diversity of human experience than it is to artificially unify that diversity into a convenient historical narrative. This also helps us to understand that our particular ancestors are, far enough back, essentially foreign to us.