Did The Soviet Union help to build the nazi army?

Not really. From what it sounds like, your teacher has conflated a number of separate, quite different, episodes and cobbled them into an unsound historical narrative.

For instance, there were German military missions to the nascent Soviet Union, but these were conducted before the NSDAP's assumption of power in Germany. The German-Soviet military relationship was not exactly one based on ideological affinities or a coherent plan. The Weimar Republic's Reichswehr saw the Soviet Union as an ideal place to train and develop equipment specifically forbidden to Germany under the terms of the Versailles Treaty. This involved mainly aircraft and tanks. The German military missions to the USSR between 1926-1933 were relatively small-scale, albeit it did provide a kernel for later German development in these areas. The Reichswehr had approached the USSR for these secret bases in the aftermath of the Rapallo Treaty and the French military occupation of the Ruhr in 1924 further underscored the need for the Reichswehr to develop modern military lest its knowledge of modern warfare atrophy.

For their part, the Red Army sought German military expertise to develop their own modern military force. The First World War and the Russian Civil War had created a corpus of combat veterans, but the nascent Red Army was bereft of officers experienced in developments in modern warfare. Wartime deaths political purges, and the promotion of officers whose political loyalty to the new regime was more important than their technical knowledge meant that the Reichswehr's professional experience was quite attractive. By the same token, German industrial firms like Krupp could produce the armor plate and other items that Soviet industry could not create in the 1920s.

The symbiosis that evolved between the Germans and their Soviet hosts was often quite frictional. While German Reichwehr officers did build up cordial relations with their direct counterparts, they maintained a consistent level of suspicion about the Soviet state and its intentions in cooperating with the Germans. There were consistent feuds over the payment for these secret bases as well as evidence of considerable Soviet spying on the German military guests. Some of this was bound to happen with a covert operation, but the ideological principles of the conservative and largely anti-communist Reichswehr ensured that the Germans did not build up a tighter relationship with the Soviets.

This part of the German-Soviet relationship ended roughly with the advent of Hitler's chancellorship in 1933. The relationship had started to cool by 1932 as the Soviets became more confident in their own abilities at conducting modern warfare and the Reichswehr began to fear it was receiving the short-end of the stick. Hitler's prioritization of abrogating the Versailles Treaty and pushing for rearmament at full speed meant that the German bases within the Soviet Union became redundant as Germany could now rearm within its home territory. Allied disarmament inspections, which were never that invasive and had very little teeth to them, had ended by the 1930s. The NSDAP's anticommunist repression and positioning itself as the foe of global communism ensured that there were few Red Army officers willing to push for continued cooperation with the Germans. The military exchange had ceased by 1933.

The Molotov-Ribbentrop Pact and the the joint invasion of the Soviet Union seemingly revived the period of 1920s cooperation. Vast amounts of Soviet raw materials allowed the German war machine to function in the campaigns of 1940 and the Germans did exchange technical equipment. But the relationship was as fraught as it had been in the early 1930s. The Soviets complained of German tardiness in keeping up their end of the pact. Germans firms also grumbled about the exchange of trade secrets and consistently dragged their heels. Although Stalin certainly played his cards close to the chest with regards to his rationale for the Pact, he did not anticipate the scale of German victories in 1940 (neither did much of the Wehrmacht for that matter). The Pact had allowed the Soviets to expand on the cheap, Finland being the exception, and steered the Third Reich's aggression towards its capitalist neighbors. But Soviet foreign policy was far from consistent. Stalin did maintain the possibility of resuscitating a Franco-Soviet alliance or a larger, neo-Popular Front with the British and French against Hitler. But the Munich Pact cast a shadow over Soviet decision making and there was a fear that the Anglo-French would make common cause with the Third Reich to push the Germans against the Soviets.

Whatever Stalin's motivations, the Germans were the only great power that took Stalin's "sale" of Soviet loyalty up in 1939. To say that Stalin's diplomatic gamble did not pay off is an understatement. The Pact helped enable the Germans to conquer Western Europe by providing the Third Reich raw materials such as oil and foodstuffs. Stalin managed to expand Soviet power on the cheap, but at a great cost to Soviet security over the long-term. And the same stresses that fractured the Weimar-Soviet relationship reappeared over the course of 1939-41. Both sides tried to derive maximum benefit from the relationship and feared that the other was gaining at their partner's expense. Yet the actual Wehrmacht itself that marched into France was constructed in Germany by Germans.

Sources

Habeck, Mary. Storm of Steel: The Development of Armor Doctrine in Germany and the Soviet Union, 19191939. Ithaca: Cornell University Press, 2014.

Moorhouse, Roger. The Devils' Alliance: Hitler's Pact with Stalin, 1939-41. London: Vintage, 2016.