I know nothing of Ms Abbott, or her children. I do know that it is a remarkable person indeed, who will sacrifice their offspring to their principals. To be honest, I wouldn't think much of someone who did. I went to a private school because public schools do an impressively poor job of educating learning disabled girls.
The headmistress of said school was a member in good standing of the American Civil Liberties Union, and the lawyer for that organization sent his daughters there, one of them was a classmate and friend of mine.
In the U.S.A. many of the upper middle class children who attend public schools spend their days in the rareified atomosphere of a "Gifted and Talented" program, where they have limited contact with the hoi polloi. The difference between a "Gifted" program and a private school is that it is funded by the taxpayers.