Barber was born on July 31, 1930, in Charleston, West Virginia, to a physician and nurse. In the 1950s he served in the United States Army as a counter-intelligence agent before attending the University of Chicago. He earned a master's degree in political science while he was there, and he moved on to receive a PhD in the same field at Yale University.

He joined the faculty at Duke University in 1972, and he became a fully fledged professor at that institute in 1977.