One example is that elite families before the Chinese revolution became elite again after the Deng reforms, even though the revolution itself was so redistributive (and repressive) that they became poorer than average during the revolutionary period: https://www.nber.org/system/files/working_papers/w27053/revi...

Other reasons are the specific predictions that a genetic explanation makes (exactly 50% contribution from males and females) which Greg Clark argues are borne out by the data; and the persistence through very different social regimes over long historical periods.

I should say that not everyone agrees, and this is just scraping the surface of the debate.

Family names are not as strongly correlated with genetics as you might be assuming.

Consider that for each generation the genetics of the family founder are diluted by 50% (assuming that consanguineous relations are excluded). So after 5 generations or so, only ~3% of the heirs' DNA is specific to the family founder.

So, the fact that names per se better predict outcomes than DNA very strongly points to social factors as the major determinants.