That's a hell of a leap of logic. If you want to attempt to make the argument that being born into money gives you no intrinsic advantages in life, that's your argument to make. Access to resources (in the modern world, money) is a HUGE advantage. I'm not jaded, I don't hate the rich nor do I want to forcibly remove their wealth, I recognize that the motive to attain wealth is the single greatest motivator ever applied to people and the primary reason capitalist societies are (by most measures) the most successful.

It's worth noting, however that the much derided and in recent history scaled back Estate Tax was originally intended to prevent the creation of a permanent landed gentry in the United States, or if you've never used that term, a group of wealthy estates that own so much they can effectively live from birth to death on the incomes of their properties. I would argue we have one, albiet not as bad as the one that inspired the law but one nonetheless.

The failing of this counterargument is that I'm not advocating for equal results of all people, I'm advocating for more or less equal opportunity. There are plenty of factors at play that we cannot control; genetics are indeed one, as are number of involved parents, upbringing, what the child is exposed to, etc. but there are at least a few that we can help control and access to capital is one of them.