I agree with your teacher, I believe the Cuban Missile Crisis was very serious and came very close to causing a nuclear war.
On 15th October, 1962, photographs were taken that revealed that the Soviet Union was placing long range missiles in Cuba.
President Kennedy's first reaction to the information about the missiles in Cuba was to call a meeting to discuss what should be done. Robert S McNamara, Secretary of State for Defence, suggested the formation of the Executive Committee of the National Security Council. Fourteen men attended the meeting and included military leaders, experts on Latin America, representatives of the CIA, cabinet ministers and personal friends whose advice Kennedy valued. Over the next few days they were to meet several times. During their discussions they considered several different strategies for dealing with the crisis. They included the following:
(1) Do nothing. The United States should ignore the missiles in Cuba. The United States had military bases in 127 different countries including Cuba. The United States also had nuclear missiles in several countries close to the Soviet Union. It was therefore only right that the Soviet Union should be allowed to place missiles in Cuba.
(2) Negotiate. The United States should offer the Soviet Union a deal. In return for the Soviet Union dismantling her missiles in Cuba, the United States would withdraw her nuclear missiles from Turkey and Italy.
(3) Invasion. Send United States troops to Cuba to overthrow Castro's government. The missiles could then be put out of action and the Soviet Union could no longer use Cuba as a military base.
(4) Blockade of Cuba. Use the United States Navy to stop military equipment reaching Cuba from the Soviet Union.
(5) Bomb Missile Bases. Carry out conventional air-strikes against missiles and other military targets in Cuba.
(6) Nuclear Weapons. Use nuclear weapons against Cuba and/or the Soviet Union.
When discussing these strategies. President Kennedy and his advisers had to take into consideration how the Soviet Union and Cuba would react to decisions made by the United States.
At the first meeting of the Executive Committee of the National Security Council, the CIA and other military advisers explained the situation. After hearing what they had to say, the general feeling of the meeting was for an air-attack on the missile sites. If Kennedy had accepted this advice it would probably have led to an all-out nuclear war.
Remembering the poor advice the CIA had provided before the Bay of Pigs invasion, JFK decided to wait and instead called for another meeting to take place that evening. By this time several of the men were having doubts about the wisdom of a bombing raid, fearing that it would lead to a nuclear war with the Soviet Union. The committee was now so divided that a firm decision could not be made.
The Executive Committee of the National Security Council argued amongst themselves for the next two days. The CIA and the military were still in favour of a bombing raid and/or an invasion. However, the majority of the committee gradually began to favour a naval blockade of Cuba.
Kennedy accepted their decision and instructed Theodore Sorensen, a member of the committee, to write a speech in which Kennedy would explain to the world why it was necessary to impose a naval blockade of Cuba.
As well as imposing a naval blockade, Kennedy also told the air-force to prepare for attacks on Cuba and the Soviet Union. The army positioned 125,000 men in Florida and was told to wait for orders to invade Cuba. If the Soviet ships carrying weapons for Cuba did not turn back or refused to be searched, a war was likely to begin. Kennedy also promised his military advisers that if one of the U-2 spy planes were fired upon he would give orders for an attack on the Cuban SAM missile sites.
A public opinion poll in the United States revealed that three out of five people expected fighting to break out between the two sides.
On October 24, President JFK was informed that Soviet ships had stopped just before they reached the United States ships blockading Cuba. That evening Nikita Khrushchev sent an angry note to Kennedy accusing him of creating a crisis to help the Democratic Party win the forthcoming election.
On October 26, Khrushchev sent Kennedy another letter. In this he proposed that the Soviet Union would be willing to remove the missiles in Cuba in exchange for a promise by the United States that they would not invade Cuba. The next day a second letter from Khrushchev arrived demanding that the United States remove their nuclear bases in Turkey.
While the president and his advisers were analyzing Khrushchev's two letters, news came through that a U-2 plane had been shot down over Cuba. The leaders of the military, reminding Kennedy of the promise he had made, argued that he should now give orders for the bombing of Cuba. Kennedy refused and instead sent a letter to Khrushchev accepting the terms of his first letter (in fact he had secretly agreed to the terms of the second letter).
Khrushchev agreed and gave orders for the missiles to be dismantled. Eight days later the elections for Congress took place. The Democrats increased their majority and it was estimated that Kennedy would now have an extra twelve supporters in Congress for his policies.
Three months after the Cuban Missile Crisis the United States secretly removed all its nuclear missiles from Turkey and Italy.
As you can see, the Cuban Missile Crisis came close to causing a nuclear war. One has to wonder what would have happened if the USA and the Soviet Union were not being led at the time by two men who were willing to negotiate an agreement.
Some historians believe, included myself, that he Cuban Missile Crisis was in fact a great victory for the Soviet Union. That the Soviets brought about this crisis in order to get US nuclear missile removed from Turkey.
For example, this is what Earl Smith, the former US Ambassador to Cuba, said two years before the Cuban Missile Crisis (27th August, 1960) to a Senate Committee looking into US Foreign Policy.
F. W. Sourwine: Is there any doubt in your mind that the Cuban Government, under Castro, is a Communist government?
Earl E. Smith: Now?
F. W. Sourwine: Yes.
Earl E. Smith: I would go further. I believe it is becoming a satellite. The logical thing for the Russians to do would be to move into Cuba which they had already done, and to take over, which they would do by a mutual security pact. Then, when the United States objects, all they have to say is: "We will get out of Cuba when you get out of Turkey."
Thomas Dodd: You are not suggesting…
Earl E. Smith: That is a speech I made in February.
Thomas Dodd: Yes, but you are not suggesting that the Communists will cease and desist from their activities in Cuba and Central and South America, or anywhere else, if we get out of these other places?
Earl E. Smith: Out of Turkey?
Thomas Dodd: Yes.
Earl E. Smith: It would mean a great deal to them if we got out of Turkey. I am no expert on Turkey.
Thomas Dodd: You do not have to be an expert on Turkey, but you ought to be a little bit of an expert on the Communists to know this would not follow at all. http://www.spartacus.schoolnet.co.uk/COLDcubanmissile.htm