It's all about the adversarial mindset, baby. Every question is binary, Either/or, yes/no, you win I lose.
Is London the centre of the universe? If the only possible answers are yes or no, then everyone who lives in london is bound to say yes, ESPECIALLY people who have moved there from elsewhere, after all, why would you put up with the squalor and the crampedness and the horrendous expense and the faff if it wasn't? The number of people who buy into the myth is a reinforcement to all the others, and everybody admires the emperor's new clothes. Meanwhile, those of us who live in the provinces resent the Londoners for getting all the money, all the attention, etc. We particularly resent the refusal of those who live in london to travel outside it - if it's the centre of the universe, after all, by definition nothing that happens outside london can be important - despite the fact that you can get to my house by train faster from king's cross than you can get from one side of london to the other.
What if we didn't think in this binary, adversarial fashion. What if we accepted that, despite it's wonders, there are legitimate valid reasons for people to live outside of London, and they don't deserve to be completely excluded from all decision-making as a punishment for this? Well, of course, intellectually, people claim that they DO accept this, and they get offended when you point out that their behaviour says otherwise. London-dweller logic is like smoker logic. If coming to meetings in london is difficult for you, the solution is easy - move to london! Etc.
How does all this apply to sexism, then? The same tendency towards binary thinking can be seen affecting gender balance. Intellectually, everybody knows that all people are individuals and deserve to be assessed on their own merits, but we can't help but be embedded with stereotypes. Women are better at some stuff, men are better at others, and the fact that the difference between members of each group is always orders of magnitude bigger than the difference between the average man and the average woman doesn't impact on most people's belief that because the average woman is better at x than the average man then THIS PARTICULAR woman must be better at x than this particular man... It takes a huge weight of evidence on the part of the disadvantaged party to get people to believe that they really ARE good at x, and they have to do the convincing every single time. And the othe similarity is that if you point out to someone who doesn't believe themselves to be sexist that they are behaving in a way that supports and reinforces this system, they get incredibly offended... And don't even get me started on racism, the very definitionn of us-or-them thinking.
I don't know what the solution to any of this is. But I'm a liberal, so I believe that there must be one, and it must be one that it is possible to persuade people to adopt.
Or perhaps I've just found another brick wall to beat my head against...