She won't give that speech because the whole narrative of her candidacy—and more broadly, her life—is as rooted in grievance as Obama's is in getting past grievance.
Her biggest supporters are the women who see themselves in her and who feel that she is/they are owed this; after all she has/they have endured. But she won't give that speech because those women don't have as much in common with her as they think. Sure, her husband's behavior has humiliated her. But she has also helped him humiliate the women he's been involved with.
She won't give that speech because she has been on the wrong side of gender bias. OK, there is no right side, but she consistently relates to and protects and stands with the oppressors in the gender wars, not the victims. It isn't only that she stayed with Bill Clinton, but that she invariably sees him as the victim, preyed upon by a series of female aggressors.
According to Carl Bernstein's A Woman in Charge, as her husband prepared to run for president, she pushed to get sworn statements from women he'd been rumored to have been involved with, statements in which they were supposed to say they'd had no relationship with him. She even interviewed one of these women herself, at her law firm. She also led efforts to undermine Gennifer Flowers, whom she referred to as "trailer trash."
In an interview she gave after the Monica Lewinsky affair became public, Hillary spoke about how horribly her husband had suffered in his childhood as the result of being torn between the first two women in his life—his mother and grandmother. (Note: Again, in this scenario it's the women who are victimizing the poor little guy.)
Hillary Clinton can't give the speech because she has not always been so sisterly, and if her biggest fans knew who she really blamed—other women—they might not still be fans.
One of the most laudable things about Obama is that he always elects to rise above the politics of victimization. One of the most troubling things about Hillary Clinton is that she is never above cashing in on it.