What led the United States and the Soviet Union to go from being allies to bitter Cold War rivals?

The US and the Soviet Union were only allies in WWII because
they were both so worried about Nazi Germany. It was not as if the two countries had any natural
reason to be allies. That means that we should not be surprised that they went back to being
rivals after WWII.

The two countries were "natural" enemies because
their systems were opposed to one another. Communist theory held that communism was inevitably
going to take over the world and the Soviets wanted to help that process along. The US,
meanwhile, thought that communism was evil and that democracy was the best system. The US's fear
of communism and its expansionist tendencies had led to bad relations between the two countries
from the time the USSR was established until the early 1930s. This enmity simply came back to the
fore when the threat of Nazi Germany was gone.

Overall, then, these
two countries became rivals because of their political/economic systems. The differences between
their systems overcame any inclination they might have had to be friendly because of their
wartime alliance.