Funny enough, I agree with both you and the person you're arguing against. I agree that the wage gap (as defined by the difference in how much men and women earn when working in the same position with the same skills) is probably pretty close to 6%. [0] I also agree that there is a big problem currently.
In my opinion, the problem is twofold. First of all, this gap - whatever you think it is, 6% or 9% or 21% - it is a problem. Most Americans live pretty close to financial ruin, like it or not. 76% of Americans live paycheck to paycheck [1] and 63% of Americans are one missed paycheck away from the streets [2]. A 6% pay gap is about two paychecks. Even though it may not seem like much to a HN reader with significant savings or a safety net, this small gap spread across the whole population actually causes problems.
The second part of the problem is societal: women are discouraged from pursuing higher-paying jobs by society. This isn't the fault of the women themselves, or the people doing the hiring, but sexism and biases hidden everywhere. In my opinion, this is the best support for affirmative action: more women doing a certain job translates to more women interested in that career.
These two things combined are a double whammy that currently mean that less women work and women who do work are not always financially secure - and that's the big problem here. If you're a woman from an upper class background and have been encouraged by those around you, you may never experience any of these problems, and that's great. But if you're an average American woman, these things have a very real impact on your life.
This also explains the giant gulfs of opinion I see here on HN. Most people here are relatively wealthy - remember, if you earn more than 36k a year, you earn more than most working Americans. $70k/yr means you earn more than 75% of American workers. I'd bet the vast majority of US programmers on here earn above 70k/yr. It's easy to get caught in a bubble and say 'well the women around me seem to have no problems!' and forget about the majority of the country. At the same time, if you live in a low-income area, those two "missed" paychecks might be absolutely killer.
[0] I have a personal, unfounded feeling that it's closer to 10% - maybe 8-9% if I had to guess.
[1] http://money.cnn.com/2013/06/24/pf/emergency-savings/
[2] http://www.marketwatch.com/story/most-americans-are-one-payc...