The leaders of the united states, the ussr, and great britain said they wanted to cooperate, so why were negotiations at the yalta and potsdam conferences so difficult?

 Each country had its own agenda about the post-war world.

Context/explanation:

Churchill in particular, along with Roosevelt, pushed strongly for Stalin to allow free elections to take place in the nations of Europe after the war. At that time Stalin agreed, but there was a strong feeling by the other leaders that he might renege on that promise. The Soviets never did allow those free elections to occur. Later, Winston Churchill wrote, "Our hopeful assumptions were soon to be falsified." Stalin and the Soviets felt they needed the Eastern European nations as satellites to protect their own interests.   So one key point of disagreement between Stalin and the other two was over the direction things would take in Eastern Europe after the war.

While Winston Churchill and Franklin Delano Roosevelt were on the same page in many ways, there were also key differences between them.   As noted by The Churchill Project of Hillsdale College, "FDR, ever the optimist, believed (or wanted to believe) that Stalin could be convinced that the West was not committed to destruction of the Soviet regime."  Churchill had a much more skeptical view of Stalin and the Soviet Union and approached the relationship in a firmer fashion.  Roosevelt had hoped to continue cooperation with the USSR.  That changed under Truman, who took over the US Presidency after FDR's death.  Truman was strongly anti-communist in his stance.

Another difference between Roosevelt and Churchill pertained to colonialism and imperialism.  Again as noted by The Churchill Project:  "Over colonialism. Roosevelt firmly believed European colonialism had been a major cause of World War I, and that it had continued to be a source of international disputes and tensions before World War II. Churchill had sworn defend the realm, which, when he took office, included the British Empire."  As it happened, after World War II, colonialism's days were numbered and independence movements broke out around the world where imperial powers had dominated.

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