The photo, taken outside the arena where Donald J. Trump’s appearance had just been canceled on Friday in Chicago, circulated far and wide: A woman in a Donald Trump T-shirt, eyes locked with a protester, her right arm raised skyward, her palm faced down.

It did not take a second glance to understand that she was making a Nazi salute. Many took the photo, published by The Chicago Tribune, as a sign of the support Mr. Trump has engendered from extremists. Others surmised that it was maybe a Bernie Sanders supporter in disguise.

But in an interview on Saturday from her home in Yorkville, Ill., Birgitt Peterson, 69, who says she was the woman in the photo, explained why she had made the salute.

She and her husband, Don, had attended the rally to check out the candidate in person. “The Republican Party needs to be broken up, and I believe Donald Trump is the one to do it,” Ms. Peterson said.

After the rally was canceled, the Petersons found themselves in the middle of a group of protesters, some of whom they described as “rude.” One was holding a poster with a picture of Adolf Hitler on it.

Ms. Peterson, who was born in West Berlin in 1946 and became an American citizen in 1982, said she took offense to the comparison of Mr. Trump to Hitler.

“They said Trump is a second Hitler,” Ms. Peterson said. “I said do you know what that sign stands for? Do you know who Hitler really was?”

“I make the point that they are demonstrating something they had no knowledge about,” she said. “If you want to do it right, you do it right. You don’t know what you are doing.”

That is when she made the Nazi salute — a gesture that is banned in Germany — as a form of counterprotest. But that is all it was, she said.

“Absolutely I’m not a Nazi, no,” she said. “I’m not one of those.”

The couple said they had not yet seen the photo, but they had received calls from family members about it.

Social media on Saturday was inundated with people sharing the photo, as well as the account of Michael Joseph Garza, who said he was the protester in the frame. Mr. Garza, in a Facebook post, said he had attempted to help the couple leave as some in the crowd grew hostile.

“I start to clear the path. I walk right up to her and say, ‘Ma’am we have listened to you. We understand this is all a little wild, but we have cleared a path for you to leave.'”

“My right hand was constantly swinging in motion, showing her the path out we made for her,” Mr. Garza wrote. “She goes, and I quote, ‘Go? Back in my day, you know what we did.'”

Mr. Peterson said the couple was upset by the accusations. “It’s insulting for anyone to assume that we have anything to do with Nazis,” he said. “We have never done anything other than demonstrate to a bunch of idiots that when they talk about Nazism, they better learn about it first.”