US War Department Pamphlet 35-3, WAC Life, May 1945
One of the most important of military courtesies is the salute. It is a respectful greeting, a sign of recognition between military persons.
It is that, and no more. There has been a good deal of misunderstanding about the salute, most of it on the part of people who don't know how soldiers feel about it. Many civilians completely misinterpret its purpose and meaning. They take it to be an acknowledgement of the soldier's inferiority to his superiors. Nothing is further from the truth. Salutes are given and returned. They are a privilege of the military alone. Every officer salutes every other officer, just as every enlisted man salutes every officer. The highest-ranking general in the Army is required to return the salute of the greenest buck private. The fact that the subordinate salutes first is simply common-sense courtesy applied to a military expression; it is for the same reason that gentlemen step aside for ladies in doorways and younger people are introduced to their elders rather than the other way around.
The salute has an additional purpose. It is evidence of respect for authority. In the Army, an officer does not determine his own authority nor just assume as much of it as he feels he should have; his authority is prescribed and becomes his duty and responsibility whether or not he likes it. In saluting, you acknowledge respect for the position and authority of the officer who holds that position.