I'm not convinced this issue has much to do with sex in general, except inasmuch as it tends to wander back and forth amoungst the sexes over time. But I do believe the issue is importent. I tend to think of the issue as "Nice" versus "Good".
Nice is a pale reflection of Good, with the rough edges filed off and all the hard parts taken out. Being nice involves a lot of lying, white and otherwise. Nice means not just allowing yourself to be bullied, but allowing others to be bullied, because "it's not nice to stick your nose where it doesn't belong". (That's a statement so vague it's only true or false (or in between!) in a specific context!)
Nice is often used as a power play: "Apologize to your aunt. They were jackasses, or even evil, but it's always nicer for the underling to apologize to the one in power," even if the one in power is 110% wrong (with the 10% coming in for willful evilness). Never say negative things, because it's not nice, even if the negative things need saying. It's not nice to question authority. Nice is frequently a major part of passive-aggressive power plays.
Nice is infantalizing to everyone, is used to enforce corrupt power structures (as in family/personal relationship power, not necessarily political power), and is (to use a metaphor that has fallen out of favor) corrosive to moral fiber. It should be done away with.
I am a fan of being Good. That's capital-G Good, as in Good versus Evil, not a nearly-content-free adjective. Good sometimes corresponds with Nice, but mostly in the unimportent areas. One notable exception is that all things being equal, it is both Good and Nice to be polite, and to assume the best about a person until you have reason not to.
But there are points of sharp divergence. "Interventions" (getting a group of trusted friends together to tell someone they are being self-destructive, usually with some sort of addiction) are not Nice, but they are frequently Good. Interventions are hard, though, for everyone involved. Checking someone's background to see whether you can trust what they are saying can be Good, even when it wouldn't be Nice. Taking stands on issues is generally Good, even when it wouldn't be PC-Nice (a particular kind of nice). (How you take that stand is another story; there are good ways to do it, and downright Evil ways to do it.)
Setting Good equal to Nice, to the exclusion of Goodness, in our internal conceptualizations is the source of some of the problems mentioned in the linked article, though by no means the only one. The interesting thing about this is how it plays out in your personal life; for instance, the bit about Nice being used as a power play comes from real-life examples, as you may have guessed. (Of course, noticing the source renders it mostly impotent...)
Nice is fairly easy. Good is really, really hard. It's painful, can be costly, and is a much higher standard in general. There's a lot of stuff in Good not even considered in Nice, like digging deep to help your fellow man and other things like that. But I'd rather live in a world full of Good people then a world full of Nice people.