I hope you'll read what Derek wrote a few times.
Let's study what you argued here: "he main point that I'm trying to get across in this article is simply that in order to create new money out of thin air, the rest of the money supply must decrease in value, which means everybody holding that money loses value which is directly placed into the newly printed money."
If everyone takes some of the new money and uses it to build their business and that business survives then their money has NOT decreased in value. You need to break out the two groups 1) Those who "borrow" some of the new money and 2) Those who don't. Yes, in a growth economy those who don't borrow lose value in their currency. But that was THEIR gamble. In a stagflation those who don't borrow money see their money go up in value. As Derek pointed out, no one is forced to play the free money game.
You say it isn't fair. Okay. Let's look at the alternative where there is no new money. Gold still backs the USD. Then what? Well, you can go visit many countries in South America and see for yourself. Two classes of people. Those with the land (gold) and those without. No growth. Just rich or poor. How much gold do you have?
Hyperinflation has little in common with inflation. This is a complex subject. If you keep reading you'll understand why that is so.
Finally, US dollars ONLY have value because you must pay taxes with them. Otherwise, everyone would be in Bitcoin. The question is, if you don't pay taxes what then? We get back to the growth question.
Money is not about math.