Weren’t the Obambi girls in a prestigious public “lab” school before they moved to their even more prestigious private Washington school?
I think the daughters went to the “lab” school run by the University of Chicago (a private school, started by John D Rockefeller in 1891), so it isn’t really public. Since both parents worked, directly or indirectly, for UC, it’s not surprising they went there, as faculty/employees’ children get preference.