Henry lived in New Jersey as a young man, graduated from Yale in 1971 and began his career in journalism in Boston, writing for the Boston Globe. His coverage of school desegregation in Boston won a (shared) Pulitzer Prize in 1975. He also wrote on the arts for the Globe, winning a second Pulitzer for his television criticism in 1980.

In the 1980s he worked as an arts critic for Time magazine, while pursuing his interests in cultural criticism and in American politics. Among his articles for Time was a story critical of the Hollywood trade newspapers in their cozy relationship in an industry town. Among his notable works were his 1984 book, Visions of America, on the American presidential campaign of that year; his 1990 video documentary of Bob Fosse, Steam Heat, which won an Emmy; and his 1992 (print) biography of Jackie Gleason, The Great One.

His final, and perhaps most notable, book was In Defense of Elitism, a work of social and cultural criticism that argued that societies and cultures might be ranked on a spectrum ranging from 'egalitarianism' to 'elitism', and that the contemporary United States had moved too far away from the latter; a view he defended with reference to college education, multiculturalism, and other topics. He died of a heart attack on June 28, 1994, while the book was coming to press.