Sotomayor is legitimately stupid and unqualified to be on the Supreme Court. She's an intellectual lightweight similar to, but not as bad as, Kamala Harris.
At oral argument, Sotomayor confused the difference between "de jure" [mandated by law] and "de facto" [existing in fact irrespective of the law] segregation.
She said "we certainly have de jure segregation. Races are treated very differently in our society in terms of their access to opportunity."
So she's wrong in two ways there. First, she means discrimination, not segregation. Second, she described de facto discrimination - which does exist and is called affirmative action - not de jure, as it isn't imposed by law. Though we all know she doesn't see affirmative action as discrimination, so she must have meant this nebulous and fictional "systemic racism" the libs always claim exists without ever being able to prove with evidence apart from "well black people do worse so that must be because of racism", when the true cause is inferior black choices and priorities.
Alito then asked "Are you aware of de jure segregation today?" knowing the lawyer would answer "I am not" because it's obvious to everyone except Sotomayor.
Rather than realize her error and take the L, Sotomayor immediately responded by doubling down: she claimed that "large swaths" of the US has "residential segregation" [nope], and that "large numbers" of schools or school districts only have one race [again, no and that would be illegal, with a handful of exceptions for black-only schools]. She then claimed "De jure to me means places are segregated. The causes may be different, but places are segregated in our country."
This is the classic "I'm not wrong, I just define the words in my own way" tactic redditors often use to transform any argument into an "unwinnable" semantic argument. In other words, it's a retard tactic. De jure literally means imposed by law. She argued [wrongly] de facto, and then called it de jure.
It's not a question of looking stupid while doing it, it's that if they were smarter, they could make more compelling arguments, maybe even peel off some of the weaker-willed conservatives (see Roberts, Kavanaugh, etc).
As it is, they are hardcore leftists and they don't make compelling legal arguments. Kagan is the one to watch out for.