Why do you think that White Europeans came to control a large share of the modern world, while those inhabiting the Americas, Africa, and Asia became subjects of Colonization?
While in other countries and on other continents people had miles of extra space, in Europe many countries and many people were squished together in a tiny area. There was much more rivalry. The people had wars and needed more area, soldiers, and resources; they also wanted to prove themselves (in this case) getting more land. Europe greatly benefited from the invasions of Mongols. Mongols brought with them various weapons from all over Asia and the Middle East (from bows to explosives). Before the Mongol Empire, Europe didn't know much about the existence of Asia and Asia didn't know much about Europe. Europeans desperately wanted more land and they got it.