The prosperity of the Western world is in and of itself enough to earn the ire of leftists. Seeing the distribution of wealth in all cases as a zero sum game, leftists assume that the West gained its prosperity through the oppression and exploitation of others, especially the third world. This idea is justification for the left to hate the West and Western civilization and to look favorably on those who use violence and terrorism against it.
But in getting down to cases the left has a problem. None of the means of oppression and exploitation allegedly used by the West on their victims are unique to the West. Slavery, for example, is an institution practiced universally, by all peoples at all points in history prior to last century. What is unique to the West is the abolition of slavery. The first great leader to speak out against slavery anywhere was Saint Patrick, and it was the tradition of Christian love for one's fellow man that was used as the rationale for movements that oppose slavery, the practice of which ended only in the West. (Slavery never stopped in the rest of the world, where it entrains as many lives as it ever did. It continues to be of significance today in Arab, African, and Asian countries.)
Colonialism in not unique to the West, either. The Turks, Mongols, Persians, and Chinese also had their empires. The degree to which imperialism contributed to the wealth of the West is debatable, and it is certainly no great source of income for western nations today. The wealthiest of all the nations in the West, the U.S.A., has never had any colonial possesions to speak of.
The West has always derived its strength not from slavery or imperialism but from its superiority in science, technology, government and commerce. The technological of western civilization superiority goes all the way back to 2000 BCE, to the emergence of proto-Indoeuropean speakers from Asia Minor, which occured by virtue of their technical prowess with the mighty horse drawn chariot. With that technical superiority in war they subjugated the known world. The Indoeuropeans almost certainly later became the ancient Greeks and Romans, and their traditions probably prefigured those of both of those civilizations. Their technical ability was combined with an ability to communicate effectively about and conceptualize technical problems, geography, numbers, and other issues important for winning wars. This ability overlapped quickly into other spheres of human activity, especially commerce. It is the market along with private property that gave rise to democracy, a form of government that is pointless without the guarantee of private property and a free exchange of goods and ideas. And from that the West has always derived its wealth, which is the wealth of its successful citizens.
To the West, slavery and colonialism eventually became inefficient holdovers from less sophisticated forms of human society. With the development of Western civilization (and only because of that development) these violent institutions were thrown aside as counterproductive. Such a development would have been possible in no other cultural tradition known to man.