And when female politicians complain about double standards in politics, they are often accused of playing the “gender card,” argued Farida Jalalzai, a professor at Oklahoma State University who published a book last year about Latin America’s female presidents.

“It’s not even subtle — it’s overt,” she said. “It’s a backlash to try to keep them in their place.”

The percentage of female lawmakers around the world has climbed in the past two decades — to about 23 percent from 11.7 percent in 1997 — but progress has plateaued, according to the Inter-Parliamentary Union, a group that promotes cooperation among legislative bodies.

“It will take another 50 years to reach parity if we continue with this kind of rhythm,” said Zeina Hilal, who studies gender and politics at the union. She said women struggled to raise money, to break into party leadership positions and to overcome the bias of voters who question the ability of women to lead.

Iván Aleite, a driver in Santiago, said he could not wait for Ms. Bachelet’s term to end. Her declining popularity as a result of a sluggish economy and judicial inquiries into questionable business deals by her son and daughter-in-law, he said, are indicative that women are unfit to run the country. “I have a theory about why Donald Trump got elected,” he said. “Americans saw the results of women presidents around the world, and the truth is that, with the exception of Angela Merkel, none of them has had the wherewithal to govern.”

Ms. Jalalzai has heard similar arguments from voters across Latin America. But if Mr. Trump’s presidency turns out badly, she argued, “people aren’t going to say he was a horrible president because he was a man.”