I simply don't accept the logic. Just because some people do well financially doesn't prevent others from doing well. One family passing wealth down generations has no effect on a poorer family's prospects. You don't make the poor richer by making the more-rich poorer.
You may not accept the logic but empirically that's the way it turns out. Of course there are exceptions at both ends of the spectrum (rich kids who fritter it all away and poor kids who make good), but on average the chances of social and economic mobility are small, and reducing.
One example of this is the "old boy" network that comes from going to a good private school. Not only do you get a pretty good education, but it seems you also get easier access to a top university and in some professions it's who you know rather than what you know.
Of course that's a rather cartoonish example but a more realistic one is that in order to buy a house in a good school catchment area you need a fair chunk of money. Less well off parents end up sending their children to less good schools which handicaps them in the game of life from the start. Now of course you could make all schools "good" but decades of all kinds of education initiatives seem to show that it's not that easy.