At an academic institute I used to work at they hired a woman whose job was to improve equality for women. One of the specific tasks was finding out why there were fewer women in the institute. She gave a long presentation showing all kinds of statistics and bizarre graphics comparing job adverts to Playstation controllers (which only appeal to men, apparently). The talk concluded with a figure comparing number of women to number of men at each stage in the hiring process. From application, to interview, to hire. The numbers were equal all the way through, with a slight bias towards women, in fact.
Every woman who was at the institute also took advantage of options that were not available to me as a man. There are special grants for women. They can apply for the ones available for me as well.
So really the question for me is why there is such a divide between the science and what people believe. It's simple confirmation bias. If you tell people that they will be at a disadvantage due to a certain characteristic then they will blame every misfortune in their life on that characteristic.
Same goes for the wage gap. We know there is no gap. It's illegal and ridiculous to suggest it exists. But you will always be able to find at least one man who gets paid more than you. As a man I don't think it's becaues of his blue eyes. But women think it's because he's a man, because that's what they already believe.