Wright's father was a veteran of the Spanish–American War, the Boxer Rebellion, and World War I, during which he commanded the 89th Division in the St. Mihiel offensive and the Third Corps. He was a recipient of the Army Distinguished Service Medal. Following the war, General Wright commanded the Ninth Corps at the Presidio and the Department of the Philippines. While his father was assigned to the newly created United States Army General Staff before World War I, Wright met William Howard Taft. Later, Wright accompanied his father on inspection tours of U.S. military installations in the Philippines. During this tour, he was deeply impressed by the naval squadron visiting Manila. His growing interest in a naval career was further encouraged by this father, giving his son a very practical perspective: