“Of course I still fancy girls.”

Those six little words, tossed off like a request to please hold the mustard, were among the most deconstructed in Tom Daley’s recent YouTube video.

Leaning against Union Jack pillows, the 19-year-old British Olympic diver continued, “But, I mean, right now I’m dating a guy, and I couldn’t be happier.”

Gay rights advocates were thrilled to welcome an out-and-proud athlete into their ranks, but the cheers were premature, or at least qualified. Daley never used the word “gay.”

Was it a disclaimer? A cop-out? A ploy to hold on to fans?

Whatever the answer, Daley’s disclosure reignited a fraught conversation within the GLBT community, having to do with its third letter.

Bisexuality, like chronic fatigue syndrome, is often assumed to be imaginary by those on the outside of the community. And 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.

But population-based studies indicate that bisexuality is more common than exclusively same-sex attraction, Diamond said, 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, 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.

Both Daley and Bello, neither of whom used the word “bisexual,” spoke of the overpowering ardor of a single relationship, rather than a shift in identity. (Bello was content to call herself a “whatever.”)

Indeed, only a handful of celebrities have embraced the term, and usually with footnotes.

Alan Cumming, who is married to illustrator Grant Shaffer, recently told Instinct magazine: “I still define myself as a bisexual even though I have chosen to be with Grant. I’m sexually attracted to the female form even though I am with a man, and I just feel that bisexuals have a bad rap.”

Cynthia Nixon, who married a woman after having children with a man, told the Daily Beast: “I don’t pull out the ‘bisexual’ word, because nobody likes the bisexuals. Everybody likes to dump on the bisexuals.”

But avoiding labels has its own baggage among gay advocates, who have relied on visibility as a weapon against intolerance.

Ellyn Ruthstrom, president of the Bisexual Resource Center in Boston, said of Nixon, “She’s very accepted within the GLBT community, but she knows that it’s a big negative to walk around saying you’re bisexual.” She added: “Many people think they can’t use the B word safely. And it’s hard in our community, because we want positive examples of bi people.”

New York’s new first lady won’t be one of those examples. When an interviewer from Essence brought up the B word, McCray replied: “I am more than just a label. Why are people so driven to labeling where we fall on the sexual spectrum? Labels put people in boxes, and those boxes are shaped like coffins.”

In Daley’s case, the difference may be generational. People who have grown up in a more assimilated world may not see the value in labels like “gay” or “bisexual,” when the communities they describe are no longer as marginalized.

“Among the younger generation, I’ve seen much more openness about bisexuality in both men and women, and often a rejection of all labels,” Diamond said.

“They’re more open to the idea that, ‘Hey, sexuality is complicated, and as long as I know who I want to sleep with, it doesn’t matter what I call myself.’ ”