Women have the right to vote and seem to engage that right at slightly higher rates than men consistently for the last few decades. http://www.cawp.rutgers.edu/sites/default/files/resources/genderdiff.pdf
Any gender imbalance in modern politics is supported by women voters. Women vote for anti-feminist positions like anti-abortion with regularity. Women voted for Trump in high numbers, despite his openly misogynistic traits. Instituting a quota would be restricting the choice of women voters, ostensibly for their own benefit. Sounds very paternalistic to me.
The problem isn't with voters, but rather barriers to entry for female politicians. One such barrier was/is rampant sexual harassment in Congress. So much so, that a taxpayer-funded harassment payout account was on the books for years (has that situation changed yet?).
And yes, sometimes we have to circumvent democracy for peoples' own good. It didn't matter how many people in Alabama supported separate-but-equal policies. That had to stop.