Freedom appeals to Americans. It is a core American value, even if it's not honored in practice here at home.
When politicians use freedom to justify war, they are making an emotional, not a reasoned, appeal. Why? It's because freedom, while a good thing, is never alone a sufficient reason for the government to commit Americans to a fight for freedom in some foreign land. The war may cost Americans more than they benefit, and America's wars have. American interventions may cost foreigners more than they gain, and America's interventions have.
To justify American interventions on grounds of reason or rational interest, the government needs to present arguments. Costs and benefits have to enter the picture. Leaders are reluctant to make such arguments for fear of exposing their war policies as lacking justification from the point of view of American welfare. When they do present their arguments, they are invariably faulty, weak, deficient, exaggerated, illogical and mistaken. They are nonsense. Leaders cannot tell Americans what their real reasons for intervention are, if indeed they themselves are aware of them.
President Truman addressed the nation several times about American intervention in South Korea, such as on July 19, 1950 and September 1, 1950. He made the case for sending American armed forces to Korea. Consequently, between 1950 and 1953, Americans lost 33,686 dead and suffered 92,134 wounded.