The reason they don't admit that they got a head start is that they actually don't believe it.

The daughter of a family friend of mine grew up middle class. Her mom was a social worker, her did had an office job. She managed to marry a man who's the son that's inheriting his dad's oil business, worth tens of millions. She is now a housewife / stay at home mom. She now has a city home, a cottage (which is fully a house, just in a more rural location) and a summer home. One of her daughters competes in sailing races (and anybody who knows sailing knows just how expensive that hobby can be), the other is into horse riding.

I've asked her what it's like for her kids to grow up rich, and she doesn't get it. She doesn't think she's rich. She says that there are houses around where she lives that are even bigger than hers, and that her husband works hard. I'm sure that's true, but she's still in the top 0.1%. And this is someone who grew up middle class, and should remember what it was like.

I guarantee that most of the kids that come from rich families have no idea what it's like not to be rich. As a result, they don't ever consider that it might not be normal to be able to have your dad's lawyer look over the contracts for your new company free of charge. They never think of how easy they had it to find investors for their company, and how forgiving those investors were. It never occurred to them that during those lean months at the beginning when their company hadn't yet started generating real revenue, that it was unusual to be able to live in their parents' spare apartment in the city, and to have dad pay off their credit card.