To their detriment. As a product of both coed and all boys private schools, there is a stark difference in teaching and disceplin in single sex schools that research shows improves outcomes. Hit http://scholar.google.com/ with "single sex education." There is a huge discrepancy in male performance especially that most teachers admit a preference to teaching girls as they "behave" better.
Bigotry and sexism exists, but the "problem" is an effect of the US obsession with political correctness and an overly sensitive and litigious society. There are cases of systematic discrimination in organizations, but they are not as pervasive as a few decades ago, so there has been progress, especially in corporate environments. An example is a female cousin with a law degree. Being a women of breading age, she was specifically asked if she intended to have children in the next 5 years which was a non-starter. These were small firms that couldn't afford to have a junior partner off for maternity leave. She had no problem with that at a large corporation.
On equality, if you start giving men maternity leave in the same way as women, and effectively change societies views on gender roles in the home, you might start seeing that form of discrimination disappear as in the scandinavian countries.
There is much to be said about differences in men and women's personalities. Normal banter between men about women kept on the "acceptable in a sitcom" when not directed at any specific women, in my view is not sexual harassment, but clearly some people disagree with that. So as long as the kid gloves are on...