I guess the main problem here is why are you starting with the idea it can be traded for gold? It cant. The answer is because they said so. Just like you cant

I guess the main problem here is why are you starting with the idea it can be traded for gold? It cant. The answer is because they said so. Just like you cant redeem it for state-hoarded lumber. See? A completely arbitrary example. “Why cant I go to the federal reserve with a million bucks and trade it for lumber?” You would ask “who told you that you could?” There was a time when the US dollar could be redeemed for gold. That stopped almost 100 years ago, and all those people that avoid discussing money in polite company turned out to grow up completely ignorant on money topics. That’s it. I’m not saying that as an insult, I am saying that multiple generations of people did each other a disservice and have outdated understandings of the concept. The US dollar is not backed by and cannot be redeemed for gold. It would be more productive to erase your concept of “backing” and “redeem for gold”, and start over from scratch, instead of trying to conform new understanding to those concepts.