There is a one-word answer to that question...privilege.
For too long, the experience of people like Alito has been assumed to be THE experience. So it doesn't really need to be understood or named, it just IS. But when Sotomayor's experience is different, it becomes problematic. It's not that she brings something additional to the judicial process. It's that we are not used to talking about the fact that he does too.
This is how white people obtain privilege in this country. Our world view is assumed to be the norm by which all things are judged. It becomes so accepted as the norm, that we don't need to define it - but it's no less there.
Years ago I had a profound experience that brought this home to me. I attended a three-day conference on "Undoing Racism." On the second day, the facilitators told us that one of the exercises for the final day would be for each of us to bring something to share with the group that expressed our cultural heritage. Many (though not all) of the white people in the group panicked...what cultural heritage???? The take-away from that experience was that our culture is the default by which "difference" is measured. And in the process, we don't even recognize or claim it.
As a white person, I am too often ignorant of the ways I make assumptions about my experience being the norm. Over the years, kind and patient people of color have given me hints about how that happens. As an example, yesterday LaAbogada gave us all the gift of a couple of examples from her own life in a diary titled What the War On Sotomayor Means to a Young Latina Lawyer. Please follow the link and read what she's written if you haven't already. She does a far better job of explaining things than I can.
I'm sure we could all tell our stories about how we slowly...painfully learn that our experience doesn't necessarily translate into a world view that incorporates ALL. I'm also sure that people of color get VERY tired of having to help us learn those lessons. And sometimes, as Nezua at The Unapologetic Mexican says, we just have to come to the place where we do the hardest thing of all...admit we don't, and maybe even can't, know.
Mi novia says that it really frustrates White people that no matter how much they know or want to know, there may be an area of experience or knowledge that they cannot access. <...>
This is another way of saying White Privilege.
How dare the world harbor some sort of Thing that I cannot experience! How dare you insinuate that you possess knowledge I may have to ask you about in humility! How impertinent of you to even imagine that I cannot, with study and great wisdom and effort, also know what it is like to grow up Brown™ in America! The voice of privilege thinks no seat is unavailable, no land unconquerable, no food untasteable, no right deniable, no experience out of reach.
Now there's some words that are hard for us to hear, right? But yes, there are some things that Sonia Sotomayor knows (from experience) about what it's like to be marginalized in this country that Sam Alito will never know. And that's why a voice like hers (added to her tremendous education and experience) is so needed on the SCOTUS.
It's also why we need to listen as much as we can to the voices of people with experiences that are different from our own as we try to craft answers to the problems and issues that challenge our country. Our vision needs to be open to incorporating a world of experiences that we haven't lived.
And while sometimes the process of learning that can be painful, it is certainly a fierce way to live. Again, I'll quote Nezua:
We are always new. Every moment is new. No moment need be like anything that came before, even when the resemblance is striking and our imagination lacking.<...>
Because life is not like a series of books in a course on ...anything. It fluctuates. We fluctuate. We are not a being, but a becoming, as Friedrich once said. And sometimes ideas are hammered out and we draw lines and walls and are told we fall on one side or the other and so do our thoughts and so does all that follows from them...and so it goes. We buy into these illusory borders, too.<...>
Being sure is but the borderwall we place around a heart to ward off the skinstripping wind of the next living moment.