Schooling, whether private or public, is so universal that there's endless different cases and motivations. The area I grew up in this was definitely a contributing factor. A lot of families sent their children to the same private school, belonged to the same country club, summered in the same places, and attended the same religious organizations. They were all culture aspects that fit together for this particular community. This can quickly lead to people spending their lives only ever in one extremely privileged bubble.