Confidence gained from their private schooling.
I'm not a rich person, but some of the people in my social circle can certainly be classed as rich, while others should be classed as "middle class but working extremely hard to send their kids to private school", and others are normal middle class who send their kids to public school (I'm in the UK here). I have no kids of my own.
One thing you would immediately notice when interacting with the kids of this fairly diverse group is that those kids that go to private school have significantly more confidence in interaction and themselves than the kids that go to public school. They are taught in different ways, and they are individually fostered and curated by their school teachers and support assistance, and they have a lot of support when it comes to "soft skills" such as confidence and interaction.
Kids who go to private school are much more confident in themselves and their actions.