Aird's father, Dr. John Aird, founded the Aird Clinic in Provo, Utah. The facility was the only hospital in the Provo area for many years. His grandfather and grandmother, William Aird and Elizabeth McLean, were Scots immigrants and the family was proud of its heritage, thus the name "Robert Burns" Aird, after the famous Scots poet. His uncle, Henry McLean Aird was a prominent educator in Utah.
A lifelong musician, Aird was president of the Cornell University Glee Club as an undergraduate, and during his tenure as neurology chairman at UCSF wrote a musical about the life of Joshua A. Norton (ca. 1815-1880), the mentally ill self-proclaimed Emperor of the United States and Mexico.