Explain how the US isn't a democracy without providing the definition of "direct democracy" and renaming that form of government as democracy to suit your argum

Explain how the US isn't a democracy without providing the definition of "direct democracy" and renaming that form of government as democracy to suit your argument. In theory, I think it's possible for an anarchist republic to exist, where there are no elections or rulers, and also no monarchy or "private" interests owning the state.