The idea that women would do a better job at running a government than men is kind of laughable but mostly immature.
If a specific woman is deserves to have a position of power, it is because she herself is qualified, just like it should be for a man. A woman has more obstacles in her path for various reasons. Some of the reasons may be misogynistic while most reasons take into consideration the many actual differences between men and women.
If women would take over the government, which social group would they come from? Is it reasonable to say that a leftist, socialist woman is more qualified than a conservative, religious man? Or is a leftist, socialist man less qualified than a conservative religious woman? My point is that a person’s gender is not what determines a person’s credibility.