Your friendly neighborhood librarian has had the great fortune of being surrounded by strong women his entire life. My mother is the rock of our family. My grandmother and my aunt (dad's sister) raised me while mom was off at work. When we moved to California, my other aunt (mom's sister) was the doyenne of the manse. I've never had a moment in my life where a strong woman wasn't a major influence on me.
My best friend, whom I met in high school, is a woman. She likewise is the rock of her family. My wife gives me what for when I act a fool. I'm a librarian, so I work in a field dominated by women. I socialize with women on a regular basis, without my wife being present. I even *gasp* imbibe alcohol with them. And, believe it or not, I'm not turned into a raging sexual beast by being around women without my wife.
It's easy to mock Mike Pence's aversion to being around women without his wife present. We can mock the idea that he's such a swinging dick that the ladies will fall all over him if he doesn't have his wife there as a shield to protect him and them. But this is no joking matter.
Pence is a man of power. Professional relationships are often forged outside of normal business channels: drinks out, dinners, other social gatherings. Pence has no problem engaging in these activities with men. But women are barred from participating in such functions. Pence might mentor a younger man one on one over a drink or a dinner; he's made it clear that a young woman won't get the same treatment. This is another barrier women face in ascending ladders of power and influence, when the guardians and gatekeepers are men like Pence.
But more than that: What does this say about how Pence views women, and the relationships which men and women can have? For a good, god-fearing Christian, Pence seems to have a very sexualized view of women. He can't be alone with a woman who is not his wife or relative because their sexual energy will tempt him to sin. Women are nothing but sexual creatures to Pence. They don't even have the option to be Madonnas; to him, unless bound by marriage or blood, they're just whores. How, exactly, is this different from a Wahhabi? If Keith Ellison were to use his Islam as an excuse to not meet women alone, the Right would be apoplectic. But because Pence is a fundamentalist Christian, he's just "living his faith".
The world in which we now live is not a world made for men like Pence. That fact is partly why his boss was able to eke out an Electoral College win. Donald Trump is the mirror image of Pence; oh, he'll have dinner with women alone, but they are as sexualized in his world view as in Pence's. Together they promised a return to a more patriarchal power structure, where men (white men) were at the top of the hierarchy, and women knew their place.
That world is gone. Barring some The Handmaid's Tale-level catastrophe, it will never return. Trump and Pence sold their mouth-breathers a bill of goods. But that doesn't mean they can't do real damage in the interim.