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You can't just name a fallacy from the wiki 'List of Fallacies' and try and win an argument.

Social status in humans and other animals is a large part genetic. This is take as fact by many people. If you believe it's not you really need proof.

The original OP didn't need to provide proof as they took it as a given and was talking a different interesting premise.

But if social status has an impact on sexual selection or individual survival then it does have something to do with genetics. It's a selective pressure meaning that genetics will likely drift in that direction.

Social status is determined by social status of forebears, intelligence, physical attractiveness, good health.

These are all heritable. This is not a matter of (formal) logic (so stop throwing 'fallacy' around); it's genetics.