Kolodny was born in New York City to Esther Rifkind Kolodny and David Kolodny. She did her undergraduate work at Brooklyn College, from which she graduated Phi Beta Kappa magna cum laude in 1962. After graduation, she took a position on the editorial staff at "Newsweek". Kolodny left to return to graduate studies in 1964, citing a desire “to teach people to think critically and because she wanted to be able to publish her own ideas, not merely report the ideas of others." Her M.A. and Ph.D. work were completed at the University of California, Berkeley, and she earned the latter degree in 1969. Her first teaching position at Yale University was cut short as she left after a year to move to Canada with her husband, whose draft board appeal for conscientious objector status for the duration of the Vietnam War was rejected. Finding a position at the University of British Columbia, she helped develop western Canada’s first accredited interdisciplinary women’s studies program before returning to the United States in 1974 to teach at the University of New Hampshire.