On Monday afternoon, the Country Music Association sent out a tweet to its half a million followers, asking, “What do you think @taylorswift13 has up her sleeve?!” Taylor Swift, one of the biggest stars country music has ever produced, had reserved time on the online platforms of Yahoo! and ABC News to make an announcement, although she hadn’t announced what her announcement would be announcing. An hour later, as anticipation built, C.M.A. echoed the impatience of Swift’s fans, tweeting, “New album? New tour? New cookie recipe? WHAT’S IT GONNA BE!?”

Once the broadcast began, Swift was seated before an excitable studio audience, like the host of a guestless talk show. She made what she called a “confession”: “I’ve been working on a new album for two years,” she said. Astute fans may have already assumed as much, given Swift’s profession and precision. (She has released a new album every other year since 2006.) She promised her fans that it would be “the most sonically cohesive* album I’ve ever made,” and she played, for the first time, a new song called, “Shake It Off,” written with and produced by two of Sweden’s greatest hitmakers, Max Martin and Shellback.

At first, “Shake It Off” might not sound very confusing. The song is an instant-retro throwback to the pop landscape of a decade ago, nodding cheerfully at OutKast’s “Hey Ya!” and Gwen Stefani’s “Hollaback Girl,” as well as Mariah Carey’s own “Shake It Off,” a big hit (and an entirely different song) from 2005 that has already been displaced in YouTube’s search results for “shake it off.” In the music video, which Swift also shared, she tries on a variety of outfits and dance moves. “I love the idea that you can tell who somebody is by how they dance,” she said, and part of the video’s charm is the delight she takes in the skill of the professional dancers and the enthusiasm of the amateur dancers who surround her. (Not everyone was charmed.)

One group of people apparently found Swift’s unveiling particularly confusing: executives from the world of country music, the genre that made Swift a star in the first place. In an interview with USA Today, Gregg Swedberg, from the Minneapolis country radio station K102, portrayed “Shake It Off” as a definitive break with the genre. “I hope she gets the country muse again soon, and we’ll gladly welcome her back whenever that is,” he said. Nevertheless, his radio station apparently can’t afford to ignore Swift and the attention she brings: the day after Swift unveiled “Shake It Off,” K102 tweeted a link to a slideshow of “25 Things You Didn’t Know About Taylor Swift.”

A similar reaction came from C.M.A. Last year, at its annual awards ceremony, the Association made Swift the second-ever recipient of the Pinnacle Award, which is meant to honor a star who has “achieved national and international prominence through concert performances and record sales at levels unique in country music,” as well as “the highest degree of recognition within the broad expanse of music worldwide.” (The previous recipient was Garth Brooks.) But after the “Shake It Off” première, C.M.A. posted a polite but ambivalent tweet: “Good luck on your new venture @taylorswift13! We’ve LOVED watching you grow!” To many readers, “Good luck” sounded like “goodbye”: the spiteful cry of a genre scorned.

C.M.A. has nothing to gain by offending Swift and her fans, and there followed a series of clarifications. The “Good luck” tweet was deleted within hours, and on Tuesday the Association tweeted, “We will never, ever, ever say goodbye to @taylorswift13. We’re STILL dancing! #ShakeItOff.” Later that day, when asked for a comment, the Association responded with a more formal statement from Damon Whiteside, a senior vice-president, explaining what had happened. “C.M.A. removed the congratulatory Taylor Swift tweet when it became apparent that our best intentions were being misinterpreted,” Whiteside said, adding, “C.M.A. is fully supportive of Taylor as she expands her reach as an international superstar.” Part of the fun of being a Taylor Swift fan is watching everybody else—or almost everybody else—scrambling to stay in her good graces.

Swift has been expanding her musical reach for years now, becoming a bigger presence just about everywhere except on country radio. The two biggest hits from her 2012 album, “Red,” were “We Are Never Ever Getting Back Together,” an emo singalong, and “I Knew You Were Trouble,” which has a bleating dubstep chorus: they reached No. 1 and No. 2, respectively, on Billboard’s Hot 100, the main pop chart, but neither cracked the Top 10 on the Country Airplay chart. (“Trouble” peaked at No. 55.) The experts at Billboard predict that “Shake It Off” will be another pop hit—they say it “seems headed for the top of the chart.” But country-radio executives will once again have to make a complicated calculation, weighing their audience’s general fondness for Taylor Swift against its desire to hear an uninterrupted stream of songs that sound, more or less, like country music.

But then, no one can say exactly what country music is supposed to sound like in 2014. And so it’s easy to disdain the genre gatekeepers who refuse to make room for a pop star who says she is determined to be led by her musical curiosity. But as the pop critic Lindsay Zoladz recently observed, disdain for generic boundaries can be a kind of orthodoxy, too. “I’ve recently started to suspect that bragging about cultural omnivorousness has become its own form of snobbery,” she wrote, “and that the new face of music-nerd élitism is not the High Fidelity bro but instead the Twitter user who would very much like you to applaud him for listening to Kesha and Sunn O))) and Florida Georgia Line and Gucci Mane and …” Likewise, maybe the new face of post-Nashville sophistication is Swift, on Monday afternoon, saying, with a trace of proud astonishment, “I’ve been listening to a lot of—late-eighties pop?”

In this context, it’s easier to see why genre loyalists can sound a bit defensive. And maybe it’s easier, too, to see why genres are useful. In a mix-and-match culture, it’s refreshing, and somewhat miraculous, that country music still exists as a genre and a radio format and a culture, able to nurture a promising teen-aged singer-songwriter with a knack for impossibly memorable love songs. A country music that can do that might also be a country music strong enough, and stubborn enough, to hear a surefire hit from one of the biggest pop stars in the world and tell her goodbye, for now.

*Correction: A previous version of this post quoted Taylor Swift as saying “confusing” instead of “cohesive.”