Dan, I think the Nixon comparison you raise applies also to another passage in Beinart’s essay:

Because women in positions of power are seen as less legitimate than men in comparable positions, a study led by Yale’s Andrea Vial warns, their mind-set can come to resemble that of “illegitimate authorities.” A “self-reinforcing cycle” develops: In the face of disrespect, a woman’s leadership style can become overly tentative or aggressive. People in turn attack her, and she responds with more self-defeating defensiveness. In their 2007 biography of Clinton, the former New York Times reporters Jeff Gerth and Don Van Natta Jr. write: “Some of Hillary’s biggest mistakes began as rather inconsequential errors in judgment and exaggerations. When they were seized on by her critics, Hillary followed—and continues to follow—the same pattern: She dug in because she feared that admitting a mistake would arm her enemies.”
Growing paranoid is easy when, because of your gender, people really are out to get you.

That last phrase of Beinart’s is, of course, a play on a phrase often attributed to Henry Kissinger about Nixon. It’s the personality of the politician that sets off the dynamic he is describing: The only stimulus the politician requires is criticism that he (or she!) regards as unfair. (Whether that criticism truly is unfair is irrelevant to the dynamic.) And, of course every politician will encounter some criticism that is unfair. Not every politician will respond to it the same way.