See Slate's complete coverage of Sonia Sotomayor.
Faced with the prospect of even trying to imagine a women's perspective, many recoil in horror. In the US, one popular trick among High School creative writing teachers is to assign students to write an essay imagining that they were to switch genders, and describe what it would be like to live for one day as a member of the opposite sex. The results are almost always exactly the same: all the girls in class write long and detailed essays demonstrating that they have spent a great deal of time thinking about such questions; roughly half the boys refuse to write the essay entirely. Almost invariably they express profound resentment about having to imagine what it might be like to be a woman.
Now I am no social scientist, and this argument may be riddled with empirical holes. But it strikes me as intuitively obvious that in order to succeed in a white man's world, women must learn to see both sides in ways that men do not. If that is true, it just might make them "better" judges, at least in some circumstances. I don't know whether Judge Sotomayor was trying, albeit rather artlessly, to make some version of that argument in her speeches about the relative wisdom of Latina woman. But if I could ask her just one question at her confirmation hearing about that Berkeley speech, that would be it.