Many of the Soviet Union's actions in the crisis over the South Korean airliner can be explained by a very simple motivation: the Kremlin's need to show the world that it is not going to be bossed around by the United States.

The latest example of this almost instinctive reaction was the cancellation by Soviet Foreign Minister Andrei Gromyko of plans to attend the United Nations General Assembly in New York this week. Rather than face the possibility of a diplomatic snub and more protests over the destruction of the Boeing 747, the Soviet leadership decided to make a virtue of keeping Gromyko at home and standing on its dignity.

The message that Moscow would like to send to Washington over the incident boils down to this: "It is no use attempting to force us to change our behavior or our policies. We intend to go on looking after what we see as our national interests, whether you or anybody else likes it or not."

Much the same message can be discerned in other public statements by Soviet officials since the downing of the airliner on Sept. 1. Whether spoken or unspoken, it provides a common thread to the Kremlin's handling of the affair and similar trials of strength with the United States in the past.

A recurring theme in official commentaries here during the past two weeks has been that President Reagan's attempts to "dictate" to the Soviet Union how it should behave have failed in the past and will fail again in the future. It is scarcely a coincidence that last week, just as the western boycott of civil aviation links with Moscow was coming into effect, the Kremlin announced that a large section of the Trans-Siberian gas pipeline was being commissioned ahead of time, despite U.S. sanctions imposed after the crackdown in Poland.

For the Soviet Union, being a superpower means never showing weakness. Experts in browbeating others, the Soviets are determined not to be browbeaten themselves.

The need not to show weakness helps explain why the Soviets shot down the plane in the first place. It explains why they reacted to what they saw as a propaganda offensive of the Reagan administration with a counteroffensive of their own. And it explains why they felt obliged to call a special press conference last week to dispel suggestions that they might be prepared to make concessions in other areas such as arms control to improve their dented public image.

Asked why the Soviet Union did not save itself a lot of trouble by admitting that the downing had been a mistake, a senior Soviet official replied privately: "To have done so would, in effect, have legalized flights by American spy planes over our territory. Our borders would no longer be inviolate."

The psychological counterpart of the Soviet Union's desire to prove itself as a superpower is a collective inferiority complex that has deep roots in Russian history. From Peter the Great on, Russian rulers sought to demonstrate that their country could emulate western achievements.

One of the best expressions of this awareness of Russian backwardness and determination to get even can be found in Stalin's complaint in 1931 that "Old Russia" had been continually "beaten" for falling behind.

"She was beaten by the Mongol khans. She was beaten by the Turkish beys. She was beaten by the Polish and Lithuanian gentry. She was beaten by the British and French capitalists. She was beaten by the Japanese barons . . . She was beaten because to do so was practicable and could be done with impunity . . . That is why we must no longer lag behind," Stalin wrote.

The remark is mentioned by Columbia University Sovietologist Seweryn Bialer in his book "Stalin and His Generals" to explain the background to the forced industrialization of Russia in the 1930s.

There is thus some irony in the fact that, in a private conversation here recently, a Soviet journalist tried to justify the destruction of the plane by recalling Stalin's lack of preparedness for Hitler's military attack on Russia in June 1941.

"For a few hours, Stalin simply refused to believe that the Germans had invaded, and we had to pay for his mistake. That is one reason why the Soviet Army is now in a constant state of mobilization," he said.

Soviet military inferiority versus the United States became painfully evident during the Cuban missile crisis of 1962 when Nikita Khrushchev was forced to back down. Soviet officials now point to that humiliation as providing the political impetus for an arms buildup in the late 1960s and 1970s.

The Soviet Union's path to becoming a superpower has, needless to say, been very different from that of the United States. While America has gotten where it is today through releasing the energies of millions of individuals, the Soviet Union has sought strength through autocracy and coercion. Individualism is suppressed and collectivism extolled.

Unable to compete with the United States in technological expertise, the Soviet Union competes instead by sheer numbers: numbers of soldiers under arms, numbers of missiles, numbers of tanks. Unable to compete through the vitality of ideas, it competes instead by the calculated use of military and political power.

A measure of the difference between the two systems is reflected in the different value put on individual human lives. At a press conference a week after the downing of the airliner, Deputy Foreign Minister Georgy M. Kornienko seemed somewhat taken aback when asked whether the "sacred" borders of the Soviet Union were worth 269 lives. His sharp reply was that they had already been worth "many, many millions of lives, as you know well."

The invocation of the huge losses suffered by the Soviet Union in World War II has been a theme in numerous Soviet commentaries on the airliner incident, and it seems to have struck a chord with ordinary Russians. Interviews conducted in the streets of Moscow suggest that most people here are quite prepared to accept the argument that the Soviet Union's security interests override everything else.

They also accept the official propaganda line that the Soviet Union must not allow itself to be pushed around by "cowboys" in Washington.