Between America and the Soviet Union, do you think one nation was more aggressive towards the other and the other nation was just reacting to its policies? Or do you think both were aggressive?
This isn't a very clear way to think about the Cold War. Both superpowers were trying to assure their own security (economic, political, and military) against the other, both did some things that could be regarded as "aggressive," both did some things that could be regarded as "reactive," both did some things that were primarily "defensive," both got entangled in wars without really meaning to, both got manipulated by third-parties at various times, both overreacted to perceived threats at times, and so on. I suppose if you went through all of the various actions/crises/events you could assign the label of "aggressive" to plenty of them and come up with some sort of tally as to who was "more aggressive," but I don't think it would be very meaningful. The fact is that both the USSR and USA engaged in a lot of very similar sorts of activities (pushing their policies onto other nations, attempting to extend their military reach dramatically, developing world-destroying arsenals, involving themselves in proxy wars, overthrowing democratically-elected governments, propping up dictatorial regimes, manipulating public perception, aggressive intelligence operations, etc.). To say "both were aggressive" also doesn't really sum it up, except perhaps as an opposition to any nationalist bromide that would make one side into an "aggressor" in a simplistic way.
The roots of the Cold War are founded in the 1917 November Revolution and the ensuing Russian Civil War. One cannot understand how either the people and leaders of the US or the USSR saw the interactions that occurred during the Cold War without knowing the previous interactions. That said, we need some brief contextualization.
Context
When in March of 1917, a semi-democratic Russian government was established after the Tsar was overthrown, the democratic allies of Russia were pleased and the United States was immediately more likely to be willing to join the war since it would not mean allying with a monarchial power. When the Provisional Government was, in turn, overthrown by the Bolsheviks in November of 1917, those governments were displeased. Their response was to give support, both during and after WWI, to those who were fighting against the Bolsheviks.
During the Russian Civil War, a conflict between the Bolshevik forces and a tenuous "alliance" of all those who opposed them, Britain and the US both not only supplied the Whites (anti-Bolsheviks) with weapons and money, but also sent troops in support. When the Bolsheviks gained complete control over the USSR, this was not forgotten and demonstrated that the democratic, capitalist nations were the enemy of the USSR and were willing to use force if necessary.
For their part, the Soviets did not endear themselves to the Western Democracies when they attempted to control the socialist parties within various other nations. Many governments saw this as an attempt at fomenting internal revolution. This, obviously, led to distrust and animosity between the USSR and the democratic states.
With the rise of fascism and nazism in Europe, Stalin feared a war with a revived Germany. In an attempt to gain allies or to forestall such an attack, he made intimations to France and Britain that he would be willing to work together to limit German power. Indeed, the USSR had a defensive alliance with Czechoslovakia prior to the Munich agreement. However, Stalin refused to protect Czechoslovakia against Germany if the Western Democracies did not also defend Czechoslovakia. When the USSR was left out of the conference and the Sudetenland given to Germany, Stalin felt that Britain and France intended to use Germany against the Soviet Union and would not uphold their assurances to Poland. He stated, "We would have preferred an agreement with the so-called democratic countries and therefore we conducted negotiations. But Britain and France wanted to use us as hired men and not even pay us anything for it."^1 It was for this reason that Stalin agreed to the Molotov-Ribbentrop Pact which allied Germany and the USSR and agreed to the partitioning of Eastern Europe.
Furthermore, once the USA, Britain, and USSR were allied after the German betrayal of the USSR and the USA's entry into the war, there was still mutual distrust. Stalin continually called for a second front to be opened so that the USSR did not have to continue to bear the brunt of the German attacks. He continued to feel that the USSR was being used by the Western Allies to defeat Germany without their having to do much.
During the conferences which occurred during and just after the war, it seems that Britain and the USA agreed that the USSR would be able to have the Eastern European states as a buffer against any future threats. However, there was still an agreement that all states would be able to hold free elections. How those two would interact was a point of contention in the future. Furthermore, the Potsdam conference finalized the agreement on how Germany would be occupied. This occupation, and its purpose, would also put the USSR and USA at odds.
The Cold War
The nature of post war Germany was truly at the center of disagreement for the former allies. The Soviets, having been invaded by Germany twice in 25 years, desired to see Germany weakened to the point of insignificance. The US, on the other hand, very quickly saw Germany as a needed ally against the looming Soviet threat. As more and more of the countries occupied by the USSR succumbed to communism (often through rigged elections or interference), the US recognized that the "free elections" which had been promised were not to be forthcoming. Furthermore, the USSR was supporting communist forces attempting to overthrow established governments in such countries as Turkey, Greece, and China.
In 1946, the United States secretary of State James Byrnes submitted draft treaties for the demilitarization and disarmament of Germany and Japan. He also gave a speech in Stuttgart regarding the depth of US dedication to a "free" Germany. The USSR analyzed the draft treaties and the speech and interpreted them as threatening to Soviet security. The foreign ministry made notes which argued that the democracies desired to reestablish fascists in Germany with the goal of an eventual invasion of the USSR. Marshall Zhukov stated,
"that the true purpose of the draft treaty is: -the desire to end the occupation of Germany and to remove the armed forces of the Soviet Union from Germany as soon as possible...in order to raise the question of the withdrawal of our forces from Poland, and in the future also from the Balkan states; -the desire to disrupt the export of equipment and manufactured goods as reparations from Germany to the Soviet Union; -the desire to preserve military potential in Germany as the necessary base for fulfilling their aggressive objectives in the future;"^2
Hence we can see that, at least in the eyes of the Soviets, US policy in Germany was a threat to their security. Future Soviet actions, such as the coup d'etat in Czechoslovakia in 1948 and the Berlin Blockade in in the summer of 1948, certainly solidified the competition and rivalry between the US and USSR. However, so did US monetary support for the regimes in Turkey and Greece in their fight against communists in their civil wars. However, each side was viewing the actions of the others in relation to their own self-interest and security. Both acted aggressively toward one another fairly early on in the conflict. The US seemed more adept at using economic forces in the struggle, while the USSR was more willing to use traditional military power.
Sources
Boyce, Robert & Joseph Maiolo. The Origins of World War Two: The Debate Continues. New York: Palgrave MacMillan, 2003.
Hanhimäki, Jussi M., & Odd Arne Westad. The Cold War: A History in Documents and Eyewitness Accounts. Oxford: Oxford University Press, 2003.
Levering, Ralph, et al. Debating the Origins of the Cold War: American and Russian Perspectives. Oxford: Rowman & Littlefield Publishers, 2001.