Some of you lack perspective. Genuine friendships between men and women were not common until maybe the last two-three decades at most, and the opinion that they aren't real in the way same gender friendships are was literally the standard. This is true in most cultures and for basically all of history until very recently. Men and women did not commonly just "hang out" in a non-dating context unless someone - usually the guy - was really trying to date the woman but didn't have the courage or honesty to say it. There are tons of study that show testosterone levels getting lower and lower for men across the board for several generations in a row, and women's hormonal balances have also changed a lot. These things affect how we think and act to a degree you may not realize. So we are becoming less different. These guys grew up before this happened and what they're saying is completely normal and standard for their generation. It doesn't make them "shut-in weebs". They're probably married and shit. They probably had girlfriends. Love isn't friendship.
That's incredibly dumb. Sorry to be so blunt, but that shit is so divorced from reality I cannot call it anything else. Men and women have had friendly non-romantic relationships as far as I can remember. And I am old as fuck. If what you are saying is true, women could have never succeeded in a professional setting because all the men would have been hitting on them non stop. Also it generally goes that a man and a woman have some type of friendly/casual relationship and get to know each other before they become romantically involved. So, what you are saying is wrong, at least from a western perspective. What happened in ancient history is completely irrelevant to a game like Persona 5, which is set in modern day Tokyo.
And the whole bit about testosterone levels is yikes.