Leon Trotsky (1879-1940) led the Bolshevik insurrection of 1917 and subsequently became Supreme Commander of the Red Army. Joseph Stalin, who took power of the Communist Party of the Soviet Union (CPSU) in the late 1920's and ruthlessly suppressed his opponents, ordered Trotsky be killed by an assassin in 1940.
For all of Leon Trotsky's momentous accomplishments in his own life, much of his legacy has, largely for reasons over which he could have had no control following his murder in 1940, not assisted the advancement of humankind.
Leon Trotsky's flawed understanding of the Second World War
After 1939, Trotsky crudely transplanted Lenin's essentially correct analysis of the bloody inter-imperialist war, otherwise known as the First World War, to the Second World War. This analysis held that no capitalist nation fighting in the Second World War was any better than any other. Thus, Great Britain, the United States, Australia and New Zealand were no better than Nazi Germany, Fascist Italy and imperial Japan. Therefore, the duty of communists in these countries was to oppose their own government's war. (In Australia, this policy was carried out by the group known as the "Balmain Trotskyists" led by Nick Origlass (1908-1996) and Laurie Short (1915-2009))
However, Trotsky drew a distinction between, on the one hand, the "inter-imperialist war", between the fascist states and the western capitalist allies and, on the other hand, the war between Nazi Germany and the Soviet Union. He still saw the latter as a post-capitalist "workers' state" in spite of Stalin's tyranny and, hence, humanity had a stake in supporting the Soviet Union.
So, whilst opposing U.S, participation in the war, Trotskyists, particularly in the U.S., supported the provision of aid by the U.S. government to the Soviet Union. A number of U.S. Trotskyists actually served as merchant seamen on the convoys which sailed through the perilous icy, U-boat-infested northern Atlantic waters to deliver cargo to the Soviet port of Murmansk.
Whether or not military action, by the U.S. Navy or Air Force, in defence of the convoys against or German U-boats or bombers would have constituted participation in the "inter-imperialist war", was not explained as far as I can recall.
Leon Trotsky's dismissal of non-Marxist political leaders
In Trotsky's world view, the only political leaders likely to be of any enduring worth, were those who fully embraced his program for world socialist revolution. Those who were not were reactionary or, at best, vacillating "petty bourgeoisie". Thus, in the Trotskyist world view, there was no merit to be found in U.S. President Franklin Rooseveldt and, or if he had still been around, President John F. Kennedy (JFK), Bobby Kennedy and Martin Luther King.
Jim Garrison could have ended the Vietnam War far sooner than the 'anti-war' Movement
This 'line' was effectively carried out in the 1960's by those who wore the label 'Trotskyist'. JFK and Bobby Kennedy were dismissed by the far-left as no better than other capitalist politicians. They chose not to dispute the fraudulent Warren Commission, which held that the solitary gunman, Lee Harvey Oswald, murdered JFK.
Jim Garrison's attempts to prosecute the murderers of JFK, as told in Oliver Stone's movie JFK (1991) would almost certainly have ended the bloody Vietnam War long before 1975 had he got assistance from just a few of the many thousands of activists participating in the protest movement. As an example, it would not have been far less likely that JFK's murderers would have then been able to murder Bobby Kennedy just as he was about to win the nomination for President of the United States at the Democratic Convention in 1968. The Vietnam War would have ended on the day of Bobby Kennedy's Presidential inauguration in January 1969, if not before.
Whatever may have been the motivations of the leaders of this protest movement, the practical outcome was the prolongation, and not the ending, of that war. The consequences for the people of Indo-China were far more tragic than they need have been.