SAN FRANCISCO — Just like countless other exercise fanatics, Chloie Jonsson wanted to test herself in a CrossFit strength competition. The increasingly popular fitness events culminate each summer with the crowning of the “Fittest Man and Woman on Earth.”

But Jonsson, who is a transgender woman, was told she would have to register as a man.

“I’ve never desired to be in the public eye and I don’t want to be the face of anything,” said Jonsson, 34, a personal trainer who lives in Los Gatos and spoke extensively for the first time about her battle on Thursday. “I just wanted to do my thing. But I’m learning that it’s not just about me.”

Jonsson’s story went public last week when she filed a discrimination suit against Scotts Valley-based CrossFit Inc. The case is focusing national attention on the re-drawing of lines about what it means to be a man and a woman in athletic competitions.

For Jonsson, who underwent gender reassignment surgery in 2006, the issue is clear-cut. She is a woman. But the fitness company, which licenses gyms throughout the world, contends that she would have an unfair advantage competing against other women.

“Their position never changed: If you were born with a penis, you have to compete as a man,” said Waukeen McCoy, the San Francisco attorney who represents Jonsson. “Their policy is you have to register with the sex you are born with. But California law is very clear that you cannot discriminate on the basis of gender identity.”

No one from the company could be reached for comment.

CrossFit’s stance is behind the times, said Helen Carroll, the sports project director for the San Francisco-based National Center for Lesbian Rights. She notes that other sports organizations — including the International Olympic Committee and the NCAA — allow transgender athletes to compete after they meet specified guidelines.

“What CrossFit has done in this case is archaic,” Carroll said. “It sounds like they didn’t even bother to Google the issue. They’re taking the approach that they just don’t want to deal with it. But it’s not going away. Everything from professional sports to club teams are dealing with diversity issues, and they’re doing it well. It’s really not that hard.”

CrossFit is a hyper-intensive fitness regimen that, according to the company’s website, has spawned a worldwide network of more than 5,500 affiliated gyms along with more than 35,000 accredited trainers. A powerful marketing tool for the company has been the annual, months-long competitions that end in July with the televised Reebok CrossFit Games.

Last year, Jonsson wanted to compete in a team event at a qualifying competition. One of her teammates sent an anonymous email to the CrossFit headquarters to make sure there would be no problem with Jonsson entering as a woman.

“I never thought they would say no, but I did think that they might need some documentation,” Jonsson said. “We were just making sure that we had crossed all of our ‘t’s’ and dotted our ‘i’s.'”

Jonsson has identified as a woman since she was 15, and underwent surgery eight years ago. Her driver’s license, Social Security card and even birth certificate identify her as female.

But CrossFit said she must compete as a male. In a letter provided by McCoy, CrossFit’s attorney wrote the company has “respect and support for Cholie’s decision and how she sees herself.” But CrossFit also is “scrupulous about ensuring a level playing field” for competitors.

“The fundamental, ineluctable fact is that a male competitor who has a sex reassignment procedure still has a genetic makeup that confers a physical and physiological advantage over women,” the letter added.

That stance betrays a misconception about the physiology of a transgender woman, said Carroll, a former college basketball coach and athletic director who has helped write policies for other organizations.

“The physical changes that take place is the transgender women loses muscle mass and has to work even harder than other women athletes,” Carroll said. “In a sport like CrossFit, the transgender woman is not in any kind of competitive advantage. She even has to work harder to maintain muscle mass.”

The suit is asking for $2.5 million in damages. But Jonsson, who said friends in the CrossFit community have been supportive of her, added that she just wants the chance to compete.

“It would just be preposterous to have me compete as a man — in a category that you don’t identify with and don’t even look like,” Jonsson said. “It would be devastating to anyone like me. And it would be the same for other transgender CrossFit athletes because there are people just like me out there.”