It was a mistake for the united states to make an alliance with the soviet totalitarian communist union during world war ii

I'll assume that's a thesis statement meant for argument or debate.  An argument could be made on either side, depending on your point of view.  

On the one hand, the United States and the Soviet Union had dramatically different worldviews.  The US system of democracy and capitalism was at odds with the USSR system of totalitarian rule and communist collectivism.  The two nations were allied only for the sake of defeating Germany and Japan in the Second World War, and were in opposition to each other in about every other way.  Following the war, they became bitter opponents in the Cold War.On the other hand, the USA and the other Allies in World War II needed the help of the Soviet Union in order to defeat the combined threat of Germany and Japan.  The USSR suffered millions of casualties due to the war -- more than any other nation.  They bore the brunt of the fighting against Germany, even before the US entered the war.  And President Roosevelt, while not in agreement with the governing philosophy of Joseph Stalin, still thought he was someone that could be worked with cooperatively.   (When President Truman took over after Roosevelt's death, he did not share that same view of Stalin and the USSR.)

So the matter can be argued from both sides.  Pick your side and write a strong essay!