“The irony is that everyone always would pat women on the head and say ‘well you know as soon as a woman is qualified there will be a woman president,’ ” Senator McCaskill said. “Now we have a stark differential in qualifications, and now it seems to be all about her integrity and how likable she is.”

In the episode, we discuss the challenges of running against a woman with former Representative Rick Lazio of Long Island, a man who discovered those pitfalls in a very public fashion. In 2000, he was Mrs. Clinton’s opponent in the race for the United States Senate seat in New York.

In a now-famous debate moment, Mr. Lazio approached Mrs. Clinton’s podium to ask her to sign a pledge, a tactic many saw as an overly aggressive male gesture toward a female rival.

Mr. Lazio told us it was a mistake that he still regrets — and one whose visual impact he underestimated in the moment.

“Our folks all thought we had won the debate hands down,” he told us. But the next day, he saw that clip played over and over again and realized that the moment was going to stick.

“The mistake that I made — and it was a mistake — was to create an optic where it looked like I was somebody other than who I was; it looked like I was invading her space and was not chivalrous,” he told us. “It was spun in the media and shown over and over again, and it looked like it was an overbearing male approaching a female.”

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