So something that is rare must be a valuable thing. Our money is based off the value of gold, so then is our money valuable because its rare as well? Even more, why must rarity be valued? I think all value come from "want." We value things because of the "pure want" if the thing.
My 2 cents....
It had been agreed on by many societies long ago that gold would be the standard that would back whatever we chose to use as money. Inherently it has no value, too soft to use in its pure form, can't eat it etc.
However, when mixed with other metal, coins were able to be made.
Prior to money, transactions were done by straight trade. I need a chicken, you need a blanket. Fine, expect I might say my blanket is worth more, because I need a chicken to eat tonight, immediately use, and my blanket would be useful to you for a long time.
You could say you'll give me 3 chickens, and I could keep the others for eggs.
That might make the deal, but, I might tell you I don't want to raise chickens, just eat one when I want to.
Having the gold coins solved the problem, because we'd be able to trade exactly what different items were worth, knowing others were now accepting these in trade. Made a lot more sense than walking around with a bunch of chickens, goats, pots and other items, trying to find someone who needed them, and had what we needed.
Of course, paper replaced gold, and more recently, plastic.
All of these things have worth, because we have all agreed they have worth. In the marketplace, we can agree to various items worth down to the smallest percentage.
Of course, we know this as supply and demand. However, I think that's how the whole thing came about, more or less.
Why did we choose gold? Who knows, and really, who cares? Could have very well been some other item that we could trade more conveniently than an old goat.
Of course individuals have different values for things. Some would give all their money, or trade a lot of their belongings, for a diamond. Happens every minute of the day when men shell out money for engagement rings.
I never had an engagement ring, and made it clear I wouldn't accept one because I personally hold no value for diamonds. The only reason I'd accept a diamond from someone is if I were able to immediately trade it for something I do value.
Today, money in the U.S. is not even backed by gold. It's fiat money. It's just been agreed upon what money is worth. That changes every day.