We are a constitutional republic, and a representative democracy. The founders knew that direct democracies are unstable and given to transitory whims, fashions, and passions. The Constitution is meant as a buffer.
If a majority of the people decided they wanted to enslave the other, IDK, say 16%, would “democracy” mean they were entitled to do so? What if the Supreme Court said that such a law were permitted by emanations and penumbrae in the 13th Amendment, these special, wicked-smaht, justices having superman like x-ray vision, not available to mere subjects of the realm?
Our Founding Fathers saw what happens in a “Democracy” in France, post-revolution.
They wanted to shield us from a “Mobocracy”!
Scalia stated re Obergefell v. Hodges, that the 5-4 majority's Equal Protection analysis was “quite frankly, difficult to follow" and “fails to provide even a single sentence explaining how the Equal Protection Clause supplies independent weight for its position." " The ruling was nothing more than a "naked judicial claim to legislative — indeed, super-legislative — power; a claim fundamentally at odds with our system of government." "A system of government that makes the People subordinate to a committee of nine unelected lawyers does not deserve to be called a democracy." - http://www.supremecourt.gov/opinions/14pdf/14-556_3204.pdf
And so, ever since the creation of the Constitution and the Republic, someones have been doing their best to subvert the intended structure. Up to now, they have done a bang-up job of perverting the Constitution having defeated most of its meaningful parts using its meaninful parts to their advantage. It is or was a Republic, if we could have kept it.