Female 'privilege' is basically the option to either become a mother / wife / career person, two of the three, or go for all of the above. Men have one option, and only one. While there are a few stay at home dads, it, just like being a crossdresser, is generally frowned upon, and unless he's rich, is often considered just a leech by many. Even John Lennon was considered a slacker for just quitting the music biz to spend more time with his family, instead of holding up the 'always be more ambitious' role that every man is supposed to.
Women don't have to, and are not expected to, always try for more pay and a higher position at work. Another 'privilege'.
I am an example of what men are expected to do; I had found a job I liked, and made good money, but was frequently questioned by both women and men, as to why I didn't try for a management position; and when it was offered, and I refused, people thought it odd that 'a man' would turn down 'a promotion'. They couldn't accept that I would prefer to keep a job I liked, rather than make more money and do something I didn't like. Men are just assumed to want to seek the most money and powerful positions possible, even if the job is awful to do; we're just expected to do it.
Women are also the ones to decide whether to accept a proposal of marriage, or refuse.
With the onset of widespread availability of birth control to women, they can also choose whether to be sexually active, or not, as well as whether to bear children, or not.

And the option to marry, have children, and sue for divorce and alimony when tired of their mate, is still generally reserved for women; men who do so, are generally ridiculed for doing that, as well.
Now I'm not saying that women have it easy in life by any means, just that there are advantages and disadvantages to existing as either sex.

Oh, and a 1990's Wall Street Journal article quoted labor stats, which showed that single, college educated women were making a mean of 101% of what college educated men were making, establishing that women who were serious about their careers, were indeed able to make the same money as men do. The women who made less? Those who choose other things outside of their career to focus on; ANYTHING that takes away focus on the career will inevitably wind up decreasing income.