One of the main human drives in life is to provide for their children. Why shouldn't you be able to spend all the resources you can to give your kids advantage?
What I find curious about this discussion, which often occurs when people discuss what advantages are fair and unfair, estate tax and the like, is that they perceive each human being as a completely independent actor. Whereas for me, at least, it's more natural to think in terms of families. If the first generation achieved success, should it be reset in the next one? Why? The example you're talking about, with people reaching incredibly high success from nothing, are exceptions; usually it takes two or three generations at least.
And it's never only about money. Family culture, outlook toward education, work ethic, etc, these things survive when the family loses all of it's fortune or goes through even more dramatic events — though it's easier to notice when you live in a country that lived through a couple of revolutions, bloody wars and a couple of genocides in the last century than in US.