If I recall correctly, the President is not a member of the military despite his Constitutional role as CinC. Clinton tried this argument during one of his many lawsuits, claiming that under the Soldiers and Sailors Act he was immune from suit. It seems the Court laughed appreciatevely. The President has authority under the Constitution, federal law, and military regulations to command the military, but he remains at all times a civilian.
The modern tradition of Presidents returning salutes started with Reagan, who had no other effective means of returning the salutes being rendered him and wanted to honor the soldiers in kind.