One of Balanchine’s most famous maxims, for better or worse, was “ballet is woman.” Yet at City Ballet, he produced a number of extraordinary male dancers, including Jacques d’Amboise and Arthur Mitchell, both 83, and Edward Villella, 81 — American treasures who overcame stereotypes about men and ballet and, on Mr. Mitchell’s part, racism, to devote themselves to the art form and to Balanchine.