Wow, okay, this is a HUGE question with a lot of complex circumstances influencing it, but I'll do my best to give you an idea of what's going on in the Soviet Union during the Cold War [I'm sure others will add to or correct the odd mistake I make].

First, Russia has had a history of invasion from Europe; whether it was Sweden in the 18th century, France in the 19th century, or Germany in the 20th century, Europeans kept expanding into Russian territory. To be fair, Russia kept expanding its territory into other regions, particularly south and east, absorbing weaker neighbors fairly quickly, but these invasions from the west were seen as a dangerous incursion into sovereign Russian territory. So, at the very least, after WWII there is a distinct belief in the imminence of another European invasion.

Second, the Soviet Union was led by Stalin at the close of WWII. Stalin was, at best, hyper paranoid about American and British intentions after WWII, especially after the Lend-Lease program ended. As George Kennan related in his famous "Long Telegram", Stalin (and his government which had become a cult of personality prone to bloody purges) was so mistrusting of the other leaders that the only way to prevent Soviet Aggression and the spread of a Communist revolution abroad was through "patient, firm containment" of the Soviet Union politically and economically. Some American hawks in the government and military also interpreted Kennan's call for containment as a military strategy; to encircle the Soviet Union with interlocking military alliances on all fronts through NATO (North Atlantic Treaty Organization), SEATO (Southeast Asia Treaty Organization), and CENTO (Central Treaty Organization) and the so-called Baghdad Pact. Encircled by what must have seemed an alliance of belligerents, the Soviet Union crafted its own treaty organization with its satellite states, called the Warsaw Pact. In many ways, the pacts just fueled the need in the Soviet Union for military might.

Third, the Soviet Union always did have a poor relationship with its Western European neighbors. In the wake of the October Revolution, some Western nations, including the United States and Britain, helped support and fund the loyalist "White" army during the post-revolutionary Civil War. The Communist "Red" army, as well as some other 'colored' armies ("Green" and "Black" armies were relatively minor players in the long run, but still significant enough to sow chaos in Russia well into the 1920s) were locked in battles that devastated the countryside and incited some pretty terrible atrocities on all sides, including forced conscription at gun point, massacring entire villages, and so on. This early experience left a bitter memory of Western powers in the minds of the Soviet leadership. And it wasn't like Western countries seemed eager to let bygones be bygones in any case as the post-Great War American society was gripped with the "First Red Scare" in which immigrants from Russia, Eastern Europe, and Southern Europe were seen - and treated - as Communist insurgents, often subject to questionable trials and spurious accusations. Politicians, for their part, were no fans of Communists and loudly made their feelings known, especially after Hitler came to power in the 1930s. Many politicians, pundits, and even celebrities/famous people like Henry Ford were openly supportive of the German dictator primarily because of his anti-Communist rhetoric.

Fourth, during WWII, after Hitler launched Operation Barbaraosa and betrayed the alliance with the Soviet Union, the Soviet Union felt it was being treated as a junior partner int he war effort. Despite efforts of FDR to smooth over relations between the three powers, Stalin complained (rightly) that the US and Britain were essentially dragging their feet and using the Russian troops as cannon fodder to grind down the Germans. And there seems to be some meat to his argument; during the famous Manhattan Project, the Soviet Union was purposefully frozen out of the creation and detonation of the atomic bomb while British scientists and government were deeply involved. It turned out to be academic in the long run because, probably suspicious of the other leader, Soviet spies had infiltrated the program and were feeding information back to Moscow on the project's potential and progress. Interestingly, though supposedly frozen out of the Manhattan Project, Stalin knew more about the project than even FDR's Vice President, Harry Truman. Keeping secrets, especially about the most devastating weapon ever created, did not dispose the Soviet Union - or Stalin - to believe in the benevolence of the US and UK; after all, the dropping of the bombs on Hiroshima and Nagasaki were not just to get the Japanese to capitulate, but also intended as a demonstration of military might to the Soviets.

Fifth, Even though a lot of the start of the Cold War was due to Stalin's personality and his perception of the outside world, it didn't end with him largely because of the factors I mentioned above; secrecy, a history of European invasion, containment, and so on. Even though Soviet leaders like Khrushchev distanced themselves in many aspects from Stalin's policies and his record, they still were surrounded by the history and the reality of their interaction with the West. To demilitarize would mean to not only jeopardize their position as leader, but also to leave the Soviet Union vulnerable to invasion. Perhaps complicating this is the fact that there was no real, direct lines of communication between the United States and the Soviet Union; when one world leader can't pick up the phone and speak directly to the other, then misunderstandings can spiral into near catastrophe, such as with what happened during the Cuban Missile Crisis. American and Soviet paranoia about each other, as well as geopolitical wrangling over the placement of medium-range nuclear missiles, almost led to a direct military confrontation between the US and the USSR - something that would have resulted in the annihilation of the human race; nuclear war. It was only after those 13 days in October, 1962 that the US and the USSR opened direct communications and began to seriously consider talks to limit, and eventually reduce, the size of their nuclear arsenals. Kind of a silver lining, but it puts into context just how 'contained' the US wanted the USSR to be - not even a hotline between Washington DC and the Kremlin existed, so how can one build trust with the other.

Keep in mind there was a lot of bad behavior on both sides - the Berlin Airlift, the Korean War, the Rosenburg spy case, and so on - which did not dispose the Soviet Union to disarm in the first place, but also there was trouble with other, non Western neighbors as well; the USSR and the People's Republic of China had a serious falling out and several wars sprung up over territorial rights and other disagreements between the two Communist governments. There were also anti-Soviet, pro-Democracy demonstrations and attempts at revolution in Czechoslovakia and Poland, meaning the idea of disarming was at best naive wishful dreaming and at worst, a rejection of the reality around the Soviet Union.

Finally, there is also the matter of national pride; your question could be stood on its head by asking why were the Americans so afraid of the Soviet Union? Why didn't the US just demilitarize? Just as the United States wouldn't THINK of disarming during the Cold War, neither would the Soviet Unin. THere are other aspects of the Cold War which go beyond, or at least parallel to, the military competition; the space race, the so-called 'peace race', and the kitchen debates are all aspects of ways in which one side said to the other "anything you can do, I can do better." At its heart, we must remember, the Cold War was an ideological battle between ways of governing and building an economy which are anathema to each other. Communists rightly argued that Capitalist economics was predicated upon exploitation of those less fortunate while Capitalists rightly argued that Communism was killing creativity and creating an inflexible market system bound for self-destruction. Politically, the US and the USSR rarely saw eye to eye and more often than not opposed each other out of spite, for lack of a better term.

Of course, there were those who tried to reform the Soviet system; Gorbechev's government shifted policies towards openness and reforms which were intended to preserve the Soviet Union while making the regime less oppressive, less rigid, and less ossified. The fact that the Soviet Union collapsed is not, I think, a result of Gorbechev's reforms per se but rather because the system was so broken by the time real reforms were implemented, that the Soviet Union was going to collapse anyway, regardless - perestroika and glasnost merely accelerated it.

SOURCES: Foreign Relations of the United States (online) https://history.state.gov/historicaldocuments/volume-title-search

Major Problems in the History of Imperial Russia by James Cracraft

Unfinished Nation by Alan Brinkley

George Kennan and Containment (online) https://history.state.gov/departmenthistory/short-history/kennan

You have to consider the fundamental political outlook of the Soviet Union: Marxism-Leninism isn't just about creating a socialist state — it's about creating an international, stateless socialist society.

The Soviet view of international relations conceived of a great struggle between capitalism (and its most evolved form, imperialism) and socialism. The USSR feared the US for the same reason the US feared communism — both saw the other as a fundamental, existential threat to their way of life.

To understand Soviet foreign relations, you have to understand the political lens through which they viewed the world. Marxism-Leninism is an inherently internationalist and revolutionary ideology. It sought to fundamentally reshape global society. The single biggest blocker to that goal are the capitalist and imperialist powers who profit from the status quo.

From Lenin's Imperialism, the highest stage of capitalism:

Capitalism has grown into a world system of colonial oppression and of the financial strangulation of the overwhelming majority of the population of the world by a handful of "advanced" countries. And this "booty" is shared between two or three powerful world marauders armed to the teeth (America, Great Britain, Japan), who involve the whole world in their war over the sharing of their booty.

Kuusinen et al.'s Fundamentals of Marxism-Leninism (which includes a version of that Lenin essay) is a vitally important text for understanding the Soviet worldview. From the text:

The Marxist-Leninist parties lay particular stress upon internationalism as one of the most important constituents of their ideology and policy.

Without internationalism, without the united efforts of the workers of all countries, it is impossible to defeat the world bourgeoisie and build a new society. [p. 305]

On a more pragmatic level: yes, during the Cold War, the Soviets were deeply concerned about the possibility of a first strike against the USSR by the US/NATO. Here's a series of sources about Soviet intentions and fears during the Cold War, produced for the US Department of Defense in the 1990s and based on interviews with Soviet officials after the fall of the USSR. They should give you some very useful insight into how senior Soviet military, intelligence and political officials viewed the Cold War.