Whatever the answer, Mr. Daley’s disclosure reignited a fraught conversation within the L.G.B.T. community, having to do with its third letter. Bisexuality, like chronic fatigue syndrome, is often assumed to be imaginary by those on the outside. The stereotypes abound: bisexuals are promiscuous, lying or in denial. They are gay men who can’t yet admit that they are gay, or “lesbians until graduation,” sowing wild oats before they find husbands.

“The reactions that you’re seeing are classic in terms of people not believing that bisexuality really exists, feeling that it’s a transitional stage or a form of being in the closet,” said Lisa Diamond, a professor at the University of Utah who studies sexual orientation.

Population-based studies, Dr. Diamond said, indicate that bisexuality is in fact more common than exclusively same-sex attraction, and that female libido is particularly open-ended. That may explain why female bisexuality is more conspicuous in popular culture, from Katy Perry’s “I Kissed a Girl” to “The Kids Are All Right” and the Netflix series “Orange Is the New Black.” (That straight men may find it titillating doesn’t hurt.)

In a recent Modern Love essay in The New York Times revealing her relationship with another woman, the actress Maria Bello wrote, “My feelings about attachment and partnership have always been that they are fluid and evolving.” Before marrying Bill de Blasio, Chirlane McCray identified as a lesbian, which has become part of the progressive credentials of New York’s first family.

Male bisexuality, by contrast, is more vexed, and much of the skepticism comes from gay men. In the aftermath of Mr. Daley’s announcement, Ann Friedman wrote a post for New York Magazine’s The Cut blog predicting that male bisexuality would become more visible as gender mores evolved. “Traditional definitions of masculinity — which tend to go hand in hand with homophobia — are going through a real shake-up,” Ms. Friedman wrote. “More hetero men are tentatively admitting that they’re turned on by certain sex acts associated with gay men.”