The secrecy of many closeted celebrities stems from a fear that revealing their homosexuality will destroy the public personae on which their lucrative and influential careers are based. This anxiety is particularly notable in the case of Hollywood stars and professional athletes, whose audiences, still prey to clichés about masculinity, can’t countenance gay heroes. But Mr. Cooper insisted that his concern was privacy. “As long as a journalist shows fairness and honesty in his or her work, their private life shouldn’t matter,” he wrote to Mr. Sullivan. “It is not part of my job to push an agenda, but rather to be relentlessly honest in everything I see, say and do. I do not desire to promote any cause other than the truth.”

What’s interesting is the assumption that simply being known to be gay could be considered pushing “an agenda”: by whom? Nobody thinks that straight journalists are pushing a straight agenda. The mere use of the word “agenda” smacks, unfortunately, of the substanceless rhetoric of the cultural right, with its paranoid fantasies that gay teachers are trying to convert straight children to homosexuality (as if such a thing were possible) as part of a gay agenda.

The privacy concern crops up again when Mr. Cooper defends his decision not to write about his sexuality in his 2006 memoir “Dispatches From the Edge” on the grounds that “it was a book focused on war, disasters, loss and survival.” But in fact a main theme of the book was that the pain that Mr. Cooper had known in his personal life — the loss of his father at age 10, the dreadful suicide, when he was 21, of his older brother — had given him insight into the pain caused by the horrors he witnessed as a CNN correspondent. To some, the omission of any reference to his sexuality in that book — surely an opportunity to reflect on sadness — seemed to betray concerns that were not strictly literary.

Like many other celebrities who have long hidden their homosexuality from the larger public while never denying it among the elites to which they belong — Susan Sontag was another — Mr. Cooper denied, in effect, being closeted. “I have always been very open and honest about this part of my life with my friends, my family, and my colleagues,” he wrote to Mr. Sullivan. “In a perfect world, I don’t think it’s anyone else’s business.” The high-minded appeal to privacy is, indeed, now a trope in the coming-out process of public figures and celebrities; Jim Parsons, the star of “The Big Bang Theory,” recently came out in an interview to a New York Times reporter who summarized the conversation thus: “he made clear that he never considered himself in the closet, per se, but was simply a private person.”

But all this talk about privacy reveals deep and troubling assumptions. Mr. Cooper compared disclosure of one’s homosexuality to revealing “who a reporter votes for” or “what religion they are,” but in a post-Freudian age in which sexuality is seen as a core aspect of identity, this comes across as disingenuous. If you’re really “happy, comfortable ... and proud” to be gay, as Mr. Cooper says he is, the simple fact of being gay should be no more a “privacy” issue than being straight is for straight people. It’s just who you are. (“Privacy,” on the other hand, would cover, say, whom you’re dating or hooking up with — nobody else’s business.) You can’t claim to be comfortable with being gay while trying to keep it a secret: When you conceal your sexuality, you’re buying, however unconsciously or reluctantly, into the notion that there is, at some level, something wrong with it.