Communism is founded on a lie. Therefore, Stalin as leader of USSR was perpetuating a lie as a means of organizing his hold on power in the USSR. His was a totalitarian government, meaning that it controlled everything about the lives of the people of the USSR. In USA and UK, there was some political control and some economic control, but most other things about life were free for people to choose or reject. In USSR, even family members where forced to tell lies about each other if the government got mad at them. Any one who is savy enough about politics to become the head of a state, knows that communism is a lie. Churchill knew this, Roosevelt knew this, and Stalin knew this. Churchill and Roosevelt distrusted the big liar, Stalin, and big liars do not trust anyone.

The primary level of mistrust that existed between the leaders was the perception of where loyalty was in the conflict.  Stalin had an agreement with Hitler, and there was much evidence to prove that what Stalin was doing to his people was actually far worse than Hitler and Mussolini combined.  Yet, FDR and Roosevelt needed Russian support to pressure the Axis forces in an Eastern theatre.  The fact that Stalin and Russia were also Communist was also a source of mistrust.  This ended up emerging after the War when both America and the Soviet Union resulted in complete mistrust with one another, carving the world between them as democratic and Communist.

The only reason the US and Britain were allies with the Soviet Union and Josef Stalin was because they shared a common enemy: Germany.  They never liked each other, never trusted each other, and even while they fought on the same side, they were conspiring and positioning themselves for a struggle with the Soviets and vice versa before the war was even over.  It was an alliance of convenience.

Stalin did not trust either FDR or Churchill, because he thought they were stalling on invading France to open a second front, trying to bleed the Russian Army by not helping as much as they could.  Actually, there is some evidence to suggest that he might have been right.

FDR and Churchill were great friends, but Churchill looked at the world like an imperialist, while FDR just didn't think that way.  So Churchill thought him naive, while FDR thought Churchill too opportunistic.

A great book about this was just released.  It's called Citizens of London.

FDR and Churchill did not trust Stalin mostly because he was a communist.  Neither man, but especially Churchill, had much use for communism.  FDR did not distrust Stalin nearly as much as Churchill did, though, and that was one reason Churchill was unsure about FDR.

Stalin did not trust either of the other two partly because they were from capitalist countries.  Communist ideology says that capitalists are a class enemy who must be fought.  Stalin was also personally distrustful of just about everyone.

FDR thought Churchill was too interested in keeping the British Empire intact.  Churchill thought FDR did not really understand Britain's strategic needs.