History

Gonna break a limb and say that big part of the reason is geography. Europe has an extremely varied geography compared to India or China, both of the latter being large landmasses without much interruption by mountains. In contrast, Europe has a very weird shape and mountains separating various peninsulae from the comparable Great European Plain (Pyrenees - Iberian Peninsula, Alps - Italic Peninsula, Carpathians/Alps - Balkan peninsula), + British Isles. Since the Roman Empire, Europe hasn't really been unified by any single political entity (other than the overarching catholic church), and even the Romans couldn't control the vast extense of the Great European Plain running from western France to the Urals, and even then relied for food on the bread basket of the great floodplains of the Nile in Egypt.

China and India, with their vast floodplains, could both feed an astounding amount of people and remain more or less unified in a single political entity for extended periods of time (reason why the Chinese consider themselves the oldest continuous civilization).

I cannot pinpoint any particular characteristic of these differences in geography and its consequences uniquely determining the history of colonialism by Europe (particularly western Europe), but for example, Germany's expansionist plans historically have had to do with conquering neighboring lands of Poland, France and even the vast fertile lands of Ukraine and Southern Russia, and less with overseas colonies the way we understand them. The same can be said of the Russian Empire, with its territorial desires reaching all of the east, part of China, west towards Poland, and south only as far as Constantinople/Byzantium/Istanbul. I guess maybe contiguous territory conquests are historically less prone to colonialism and more people to expansionism and assimilation, and overseas are more prone to colonialism?