the last argument you'll never get to win, settled by people who outlived you
means the money, property, or traits passed down to you from someone who has died — or, more broadly, anything handed down from the past.
from From the Latin 'inhereditare,' to make heir to, built on 'heres,' an heir — the one who 'takes' what's left. It reached English through Old French 'enheriter' in the medieval period, when land and title passed strictly down bloodlines and an inheritance could decide your entire life. The 'in-' is an intensifier, not a negative: it means 'into' the estate, not out of it. The biological sense — inheriting your father's nose or your mother's temper — is a much later borrowing of the legal idea, as if your genes were an estate quietly probated at birth.