But wealth, along with a solid education, a well-developed relevant skill in the marketplace, a well-established social and professional network, and a family with a good reputation can be much more persistent.

The claim is that most of that is biology and heritable. Your ancestors had good genes (again, IQ but not only) which allowed them to gain a skill in the marketplace, construct a social network, create a family with good reputation, and acquire wealth. You have skills in the marketplace, able to adroitly navigate society, etc. primarily because you share genes with your ancestors, not because you inherited some money.

my parents ... taught me

This is the nature vs nurture debate and lately the nature side has been winning. Who and what you are is considerably more determined by your genes rather than by your upbringing. Gwern posted about this here, on LW, or you can google up twin studies (studies of (genetically) identical twins who were separated at birth and brought up by different people in different circumstances).

Can you give me some examples of how "culture persists across generations"?

See e.g. Yvain's review of Albion's Seed.