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What were people fighting for in World War II?
Well, that's a big question. First of all you have to distinguish between what states were fighting for, what their populations were fighting for.
Hitler made his own goal quite clear very early: conquest, Lebensraum (room for living) in the east. The German people were expansive and they needed room to live in and that room would be cleared of the populations, the Untermenschen (sub-human) populations in the east such as the Slavs. He defined this conquest largely in racial terms. In the initial stages of the war, after conquering Scandinavia, Denmark, the Netherlands, and eventually France as well, the conquered territories were placed under the control of Nazi Germany with the explicit idea of exploiting their resources in the service of the war machine.
This meant that in the east after 1941 when the Nazis invaded the Soviet Union that this racial expansion produced a war that was defined racially, a war of extermination. The Eastern Front was in many ways the most bitter theater. It's the place where the Holocaust largely took place, where the Slavic peoples in Eastern Europe faced the horror of a conquering army that had defined them in subhuman terms.
What were the Soviets fighting for? Well, they were fighting to save their revolution. Stalin was remarkably successful when you think about the fact that in the 1930's he hobbled his economy with the collectivization of agriculture, introduced a crash course of industrialization in certain areas, and then the Great Purges, including many of the most experienced military leaders in the party. In spite of all this, Stalin managed to mobilize the population. And here it was kind of a Soviet nationalism that emerges, a successful one that rallies a population that had been traumatized in so many ways to defend the nation.
What were people fighting for in other parts of the world? The United States and Britain signed a document written in the early years of the war called the Atlantic Charter wherein they defined their goals in terms of the defense of democratic principles, in particular the principle of national self-determination. In that sense, the Allies were fighting in defense of democratic principles and you have to recognize that as late as 1942, this may have looked like a losing proposition. Liberal democracies hadn't fared very well in the interwar period. They'd been hit hard with a depression; capitalism itself seemed unstable and incapable of regulating itself; and the liberal democracies in Europe had been powerless to prevent Hitler and Mussolini from taking power. At this point, liberal democracy seemed like an ideology of the past, while the two dictatorships - the Soviets on the left, the Nazis and Fascists on the right - seemed to be the ideologies of the future. Of course, standing up for national self-determination in 1940 was not uncomplicated for the Allies. The British were an empire. What did it mean for the British to stand up for national self-determination at this point?
The question about what people were fighting for is a question that the social historians of war will debate endlessly. People fight for all sorts of things. They fight for their families, for their community, and for their local religion. They may or may not be motivated by certain ideologies. Take my own field, French history. If you look at what motivated people to join the Resistance during the German occupation, there were all sorts of people. There were communists who were fighting to defend the Soviet vision of revolution. There were monarchists who were organizing a nationalist response to the German invasion. People within these societies came up with their own justifications for their struggle.
By 1945 the members of the Allied Coalition could congratulate themselves on having achieved the freedom of European nations by defeating the Nazi military machine. But it was still a freedom complicated by a set of concerns about the postwar period. The Western Allies had moved across France and into Germany while the Soviet forces had done the same, meeting in the middle. Already, at the end of the war, it was clear that the governments in the west, as well as the governments in the east, were jockeying for position in a new confrontation that would become the Cold War.