The full video is here, if you want the context (though clearly you weren’t interested in the full context before leaping to judgment).
She was talking to students about jobs and clerkships. She noted that if you want to work for “legal defense funds”–which is shorthand for impact litigation organizations–an appeals court is the place to get relevant experience. Impact litigation is the practice of bringing certain cases not for the effect on a particular client, but for the effect on the law and ultimately on public policy. From the NRA to the NAACP, many organizations seeking political change also do so by means of impact litigation. The DC guns case (Heller) is a classic example of this. Clients are carefully selected, and the case is managed and timed to present the best possible argument for a change (or a beneficial clarification) of the law.
Impact litigation focuses on getting into appellate courts, and that tends to be where the real battles lie, because the effect of a win in the district court doesn’t have the kind of impact that an appellate court has. Additionally, anything that is in a gray enough area of law to be good fodder for impact litigation will almost inevitably be decided by an appellate court. By virtue of working with more complicated, less settled issues, appellate courts also have to employ more subjective judgment. They have less precedent to rely on. They make law in a very real sense, and that law usually has important policy consequences. In that sense, they make policy.
You’re confusing “making policy” with deciding disputes based on policy. Courts undoubtedly make policy, as Sotomayor states. But that doesn’t mean that judges decide based on policy preferences. She’s merely saying that if you want to work go work for any of the dozen or so elite impact litigation organizations, it is very useful to have experience working for appellate judges to understand how the appellate court works, how appellate judges make decisions, etc. She’s giving good and true advice.
What you mistake for embarrassment is nothing of the kind. She’s recognizing that while her audience understands her meaning plainly since as law students they understand the context, the wider public might misunderstand what she means by making policy (especially if the quote is taken out of context). She is saying something that every lawyer knows, even if they don’t admit it, so she sort of does so with a little wink and a nod and an acknowledgment that in the age of shrill cries of judicial activism, people will likely misunderstand what she means when she says appeals courts make policy.