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I don't doubt that there are elements of sexism involved here, but it is also clear that a lot of men wouldn't have backed down so easily.
Politics is a tough business and you gotta let a lot of s--- roll off your back, even if that includes personal (and let us say ridiculous) insults and threats (which should be turned over to the legal authorities).
Some of what I see in this piece is the result of inexperience. Some of it is the shock of being hit hard and being accustomed to playing nice instead of coming out swinging.
It's too bad that the Edwards campaign didn't pull an experienced strategist to lend a hand in fighting back, but, as noted, personal lives become public in politics. It is a huge mistake on the campaign's part though, because, if they'd hit fought back on this issue, they could shown that they are tough and aren't going to put up with nonsense. That might have spared them some crap down the road.
Now their opponents know that they just have to make the girls cry and the campaign will whimper in the corner.