It's a common thing rightwingers say—"America is a republic, not a democracy!"—because they know at some level that their ideas are not popular and that if elections in the USA were actually fair, they could never win. I think it's true, though, that amerikkka is a republic—a slave republic, just like Athens and Rome, where the only people with any kind of political power are the ones who got rich by crushing everyone else.

Tell them that, while the "archy" of words like oligarchy means "rule" or "command", kratos means "power" or "strength", and that demos is "the common people".

A true democracy, therefore, is not rule by the majority—that would be ochlarchy or, more commonly, ochlocracy, ochlos being the "masses"—but an empowerment of the common people.

And that they're right, America is not a true democracy.