Why did relations between the USA and the USSR break down in 1945?

The reason was best described in 1835 by one Alexis de Tocqueville in "Democracy in America."

"There are at the present time two great nations in the world, which started from different points, but seem to tend towards the same end. I allude to the Russians and the Americans...

All other nations seem to have nearly reached their natural limits, and they have only to maintain their power; but these are still in the act of growth... The Anglo-American relies upon personal interest to accomplish his ends, and gives free scope to the unguided strength and common sense of the people; the Russian centres all the authority of society in a single arm. The principal instrument of the former is freedom; of the latter, servitude. Their starting-point is different, and their courses are not the same; yet each of them seems marked out by the will of Heaven to sway the destinies of half the globe.”

Exceptions to the above "rule" occur when the two have one or more common enemies. Up to 1945, these consisted of Germany, Italy, Japan, and a few east European nations. In the 1860s, Russia was still "smarting" from its defeat in the Crimean War by Britain, France, and others. It was then very friendly with the United States, who feared British and French recognition of the Confederacy (and later sold Alaska to the reunited U.S.to create a "buffer zone" between British Canada and Siberia)

In 1945, the "common enemies" disappeared, and America and Russia reverted to the "Tocquevillian" order. They will become friendly again if and when there is a common "third" enemy (e.g. China).

The USA (democracy) and the USSR (communist) were diametrically opposite of each other. They had very little in common. Very different ideas how the economy should work.

Their alliance was one of necessity. They needed each other to defeat the Axis powers. Once that was achieved, it was a matter of time before they became political enemies.

The Americans send an expeditionary force to Siberia in 1918. They withdrew that force in 1920. Mainly because the communists had won the civil war. The relations between the two were not 'the best of friends' to say the least in the 30's.

Ideology was secondary, spheres of influence were primary reason for geostrategic rivalry

Before WW2 both the US and the Soviet Union were more regional than global powers. The US had great influence in North and South America (Monroe Doctrine), but almost no political influence in Europe, and only limited influence in Asian Pacific region due to other powers like Great Britain and Japan. TheSoviet Union, as the only socialist country, had some global influence through various leftist movements, but this was limited. In Europe, other powers (Great Britain, Germany, France etc ...) effectively blocked the Soviet Union, and only after the start of WW2 did the USSR managed to act locally in Finland and Romania (Bukovina). In Asia the USSR clashed with Japan over Manchuria and Mongolia, and had some influence in Central Asia. Although across from one another at the Bering Strait, the USSR and the US didn't have much contact and were not seen as opponents despite different ideologies before WW2.

After WW2 things changed dramatically. Both Germany and Japan disappeared as great powers. France was severely weakened, and so was Great Britain (the British empire collapsed soon after.) Although badly hurt in the war, the Soviet Union was now the undisputed victor in the eastern part of Europe, and ideologically aligned itself with numerous leftist liberation movements in Asia (themost important of these being China.) The US became the leading power in the West and effectively succeed Great Britain. In fact, after WW2, Britain was practically unable to have an independent foreign policy (as witnessed, for example, in the Suez Crisis) and become a US junior partner. During the war, Churchill and Stalin agreed on zones of influence in post-war Europe, now British zones simply became US zones. In China, both the US and the USSR had their favorites, and the Soviets won. There were also divisions in Korea and Vietnam, which later led to wars.

Although ideology appears to be at the forefront of the conflict, in reality it was not so. For example, the US (supposedly champion of democracy) often supported various monarchs and dictators in order to thwart the Soviets. They were even ready to support communist China, after the Sino-Soviet split. The Soviets, although nominally more ideological, didn't shy from helping completely anti-communist regimes when it suited them. For example, in 1980 Argentina increased exports of food to USSR, despite other countries in Western hemisphere boycotting it because of Soviet intervention in Afghanistan. To return the favor, Soviets abstained in voting for Security Council resolution 502 and allegedly helped Argentinians in the Falklands war with some recon assets.

As a conclusion, we could say that after WW2 both the US and the Soviet Union became global powers with conflicting interests in various parts of the world. As other countries joined one or the other side conflict intensified and became the Cold War. Ideology was an important part of this, but it was not the deciding factor - after all, Russia is no longer a socialist country, yet it is again opposed to the US, although ideologically and culturally much closer to it then, for example, the US ally Saudi Arabia. Rather than that, strategic interests decide who would be ally and who would be foe.