The answers so far are not answering the question. People are saying why they believe communism is morally wrong, not why Americans believe it is evil.
The American Cultural Context
The simple answer is that America has always been suspicious of foreign ideas, especially those which conflict with values considered quintessentially American (WASP). Manifest Destiny is still an important influence on how Americans think about their country and the world. America is believed to be uniquely special, and foreign ideas can only dilute the country's purity.
There have been two Red Scares in American history. 1917-20, and 1947-57. As the Cold War went on fear of communism intensified, and was a primary motivation for involvement in the Vietnam War.
As he [JFK] told senator and Vietnam skeptic Mike Mansfield after the Cuban
Missile Crisis, "If I tried to pull out completely now from Vietnam,
we would have another Red scare on our hands." In July 1963 he is said
to have told reporters at an off-the-record news conference: "We don't
have a prayer of staying in Vietnam.... But I can't give up a piece of
territory like that to the Communists and get the American people to
reelect me."
Hostility to communism lingers because of the American character, which hasn't changed much over the last century. America's core values remain religious, and for economic and personal freedom as they understand it.
Americans today are far more religious and individualist than their peers in other developed nations. Consider this analysis by Pew Research. Also consider this data from Gallup. America's most religious states are as religious as Iran, India, Iraq, while America's least religious states are twice as religious as the least religious countries in the world, Estonia, Sweden, Denmark, Norway, Czech Republic, Japan, France.
As a result of all this, Americans are usually hostile to atheists and collectivist ideas. Communism happens to be very atheist and very collectivist.
Meanwhile, Elsewhere
But this is a distinctly American psychology. Many other cultures value collective responsibility, and regard self-expression with apathy. Japan is perhaps one of the best contrasts, but it's also true to an extent in places like Germany and Scandinavia (consider the Danish Law of Jante). In 2009 Der Spiegel published an article which found half of East Germans were sympathetic to the former communist dictatorship.
Today, 20 years after the fall of the Berlin Wall, 57 percent, or an
absolute majority, of eastern Germans defend the former East Germany.
"The GDR had more good sides than bad sides. There were some problems,
but life was good there," say 49 percent of those polled. Eight
percent of eastern Germans flatly oppose all criticism of their former
home and agree with the statement: "The GDR had, for the most part,
good sides. Life there was happier and better than in reunified
Germany today."
In former Soviet states, most notably Belarus, the Communist past is regarded as something largely historical rather than evil. Without the Red Army, the people of Belarus would have been annihilated by a roaming Nazi genocide.
The headquarters of the Russian Social Democratic and Labour Party was founded in Minsk, and so Belarusians have a deep relationship with Communism and Soviet security forces. I've visited Minsk, and there are museums dedicated to the Great Patriotic War and the Belarusian police force (exhibits explaining their involvement in the war, Chernobyl, and Afghanistan).
This is quite the contrast to examples like Hungary's House of Terror, which makes the point that Nazism and Communism are equivalent evils. In Belarus there are statues of Lenin everywhere, while in other former Communist states Lenin was removed swiftly after the collapse of the Soviet Union. The difference depends upon whether the Soviets are regarded as liberators or invaders.
The Ethical Imbalance
Often rejection of communism is post-rationalised ethically. Given the aforementioned, there are common references to a communist state "stealing" from the individual, but this is not a universal belief. Many cultures appreciate communal interdependence; meaning the idea that a collective "steals" from the individual is absurd, as the individual's wealth creation is dependent on the collective working together.
Examples of Anti-Communist terror are rarely acknowledged. Consider Suharto's purge of Indonesia in 1965 resulting in a million deaths, or the Dirty War in Argentina resulting in 30,000 "disappeared", or the Vietnam War resulting in two million civilian deaths.
The other issue often brought up is the death toll produced by Communist states. Obviously this is factual, but in the Cold War it was not one sided. The truth is that both the USSR and USA were responsible for mass-murder, committed to enforce their regional influence.
The above image was taken in New York City. The implication here isn't that Communists are worse because they killed more people. It's that Communism is uniquely murderous, which isn't true. This also doesn't explain anything. An honest tally comparing the death toll of different ideologies would produce a very different message (perhaps a better one; that dogmatism leads to intolerance and murder).
Furthermore, both Communist and anti-Communist forces engaged in state terror. Consider the brutality inherent in Communist systems, and also the brutality inherent in the states America nurtured in Latin America through Operation Condor. Argentina's dictator General Jorge Rafael Videla claimed to be fighting terrorism and said:
A terrorist is not just someone with a gun or a bomb, but also
someone who spreads ideas that are contrary to Western and Christian
civilisation.
This was typical amongst the juntas endorsed by the United States, and led to systemic state sanctioned abduction, torture, rape, and murder. When Chile's military launched a coup to seize power from the failing socialist government, the junta did not revert to constitutional norms, as the country's right wing wished, but suspended the constitution and banned political parties and trade unions.
Of Dominos and Dissidents
For over a hundred years, Communism has been one of many totalitarian ideologies. Fascists in Italy, Germany, and Spain were viciously anti-Communist. The Nazi party believed Communism and Liberal Capitalism were two sides of the same Jewish coin. During the Cold War, being anti-Communist was a convenient excuse for American endorsement. Apartheid South Africa was very Protestant and very anti-Communist, fighting against Communists in Southern Africa to expand their influence. Saddam's Iraq was anti-Communist, Baathists in Iraq and Syria considered Communists and Islamists to be their nemesis. The Baathists despised the anti-religious character of Communism, and the anti-Nationalist character of political Islam.
It was dangerous to be a Communist in America, just as it was dangerous to be a Liberal in the Soviet Union. Both nations sought to subvert dissent, internally and externally, in spite of constitutional norms.
This intolerance at the cost of constitutional norms and freedoms wasn't just exported. Between 1956 and 1971 the US government ran COINTELPRO, a secret and illegal project by the FBI to discredit and destroy political movements deemed a threat to the status quo. The FBI was concerned about the rise of a 'black messiah'; a charismatic black liberation leader able to unite working class black and white communities, which would have significant political consequences for domestic and foreign policy. Of the individuals the FBI considered possible candidates, most were killed (Martin Luther King, Malcolm X, Fred Hampton, the latter unambiguously murdered by law enforcement). This wasn't the only time an American government would break their own rules to spite Communism, Iran-Contra being another obvious example.
Many Americans however tolerated these abuses of power, because they feared Communism would deprive them of their economic and religious freedoms. Domino Theory became an enduring way of rationalising Cold War paranoia. According to this geopolitical hypothesis, Communism was essentially infectious, and its existence anywhere threatened to spill across borders. This anxious conclusion guided policymaking for successive American governments, from Eisenhower to Reagan.
The concern that Communism would take away American liberties wasn't without basis, as Communist states uniformly advocated state atheism, and mostly banned private ownership and freedom of expression. Cuba undoubtedly contributed to an American belief that Communism meant economic collapse. And yet, Fidel Castro's government had more in common ideologically with the French Revolution than the Russian. Soviet advisors gave the new Cuban government economic advice... which was completely ignored. The Cubans experimented with a uniquely Cuban sort of Communism. They visited the Soviet Union and China, and found both models lacking. Their own design was more far-left than the Soviet Union, and an unmitigated economic disaster.
On the other side of the Iron Curtain, Soviet leaders were anxious that liberalisation would mean the end of Communism, and thus exploit the people via unregulated robber baron capitalism. These concerns were not without basis either. The threat of liberalisation, even within the context of an essentially Communist system (i.e. Czechoslovak 'Socialism with a Human Face'), invoked military interventions by Soviet forces on multiple occasions. Notably: East Germany in 1953, Hungary in 1956, and Czechoslovakia in 1968.
Both Communist and anti-Communist forces engaged in murder, torture, terror, and suppression of political freedoms and human rights. So it can't just be that Communism suppresses political freedom or tortures its enemies. The reason Americans disapprove of Communism is elsewhere: it is because of an emotional reaction to ideas which clash with those they have internalised.
This also explains why Americans do not discuss things like Operation Condor, when weighing the question. Regardless of the fact that any sort of dictatorship in Latin America (or elsewhere) is evil. But one evil is regarded as more so because it is less familiar.
For most Americans Communism is culturally incompatible.