Why is the word "democracy" not in the preamble of the US Constitution?

Why? Try these on for size:

When the people find they can vote themselves money, that will herald the end of the republic.

—Benjamin Franklin

‘Karate Kid: Legends’ Gets Kicked Around in Box Office Bow by ‘Lilo & Stitch,’ ‘Mission: Impossible’ - The Hollywood Reporter

—John Adams

—Alexis de Tocqueville

To Indians: “Pack up what belongings you can carry and start walking to Oklahoma. Your fertile lands are ours now. We voted fair and square and your side lost.”

Would you join a gym or workout at home and why?

[with republicanism being the rights-protecting form of governance afforded us by our Constitution]

Meanwhile, when the Democratic Party formed in 1828, it was with a Tory outlook keen on robbing others of their rights:

Another tendency, which is extremely natural to democratic nations and extremely dangerous, is that which leads them to despise and undervalue the rights of private persons.

John Harbaugh on Aaron Rodgers: I don’t have a reaction, just respect - NBC Sports

I do not say that democracy has been more pernicious on the whole, and in the long run, than monarchy or aristocracy. Democracy has never been and never can be so durable as aristocracy or monarchy; but while it lasts, it is more bloody than either.

The republican is the only form of government which is not eternally at open or secret war with the rights of mankind.

To slaves: “You can forget your notions of freedom. We voted fair and square and your side lost.”

Thin, Light and Built to Last: The New Era of the Galaxy Z Series - Samsung Newsroom

In other words, our Founding Fathers and other Whig intellects of that time well understood that democratic methods are the surefire means to do serious damage to the rights guaranteed under republican self-government.

Majority-rules democracy is the way that majorities run roughshod over minorities, destroying rights and all ideas of equality under the law. No fair-minded person wants anything to do with democracy.

—Thomas Jefferson

How is the legalization of same-sex marriage impacting societal norms in the USA?

To blacks: “You can’t drink from that water fountain… eat in this cafeteria… ride this bus… go to this school. We voted fair and square and your side lost.