Okay, that explanation is better, but you're still leaving some genuinely complex terms dangling there. Ownership still isn't explained beyond the declaration that is is necessary to make stuff. Price and Money have no introduction at all.

I skipped money and price in my explanation, so here:

People that owned stuff they didn't use had a problem where the stuff would decay and rot and they would no longer have as much stuff. So they were willing to give others stuff that rots in exchange for stuff that doesn't rot, and ideally that didn't take up much space. Gold and silver proved to be ideal; inherently useful as a plate or goblet that lasts forever and doesn't poison you, compact, and easy to store forever.

Because the owners that own most are ones that were ruthless in getting more, owners very reliably wanted gold and silver. People that made stuff were willing to take gold and silver instead of the stuff an owner had because they knew other owners would be willing to give them stuff in return that the owner that gives them stuff doesn't have.

A downside of gold and silver is that they can be mistaken for other metals owners didn't want as much, so owners started giving people gold or food to check if the gold and silver were pure, and to stamp a promise that it's pure and how much it is into it. A convenient way to make this stamp fraud-resistant is to make it as big as the lump of gold or silver, to make the lump flat, thin and a certain width, and to stamp both sides. This is called a coin. This way it was very hard to remove any gold or silver from the coin without it showing as the pattern of the stamp being broken.

At this point, the gold and silver were pretty useless in their own right - you can't eat off a coin - but people still expected owners to want them because those owners would probably expect other owners to want them. They were wanted because people expected others to want them. Coins and this commonly held expectation of their worth was called a currency.

This went wrong as often as you might expect - owners convincing certifiers to lie (debasing te currency), people finding lots of gold causing people to be able to get less stuff for the gold they have than they expected when they accepted the gold (inflation), and more - but in the end the expectation came back because the owners that owned the most kept being the ones that wanted to own the most.

Eventually, owners had so much stuff that it became a hassle to carry all their gold and silver around, so they started writing notes promising to give whoever held the note gold, and offering those notes to people instead. These notes are called 'money'. The more gold owners had, the more reliable it was that they could make good on that promise, so when states came along their notes became the most reliable.

States started threatening to beat people up if they did things or give things without publicly announcing what amount of money they would be willing to do that for and always doing it if someone offers them that money (except in state-outlined exceptions). This announced amount is called the price of the thing.

Then they said they didn't want to give people gold for money anymore because the promise to get something for a price was reliable enough instead. This is called "fiat currency". Then they started printing money whenever they felt like it.

It is perfectly acceptable to assume that, like the vast majority of educated adults, the audience will understand the term “private property”.

There is a difference between understanding the term "computers" and understanding computers. I can explain the former but not the latter. Most people understand the term "private property", but their understanding of private property is barely functional.

Perhaps that's where this conflict is coming from. The OOP asserts something about explanations of capitalism, and you want that to apply to explanations of terms or to barely functional shallow explanations.

Of course I can explain something deceptively if I do a bad enough job. That's an ambiguity in the phrase "can explain", I suppose. Like saying you "can run a marathon" if you can hike 42 km in four days. If you're looking to argue in bad faith I could see how that would be an in for you.

You refer to a “term-free” explanation. What is the definition of a “term”, and how would an explanation every be free of them?

(figurative) demonstrations can be term-free explanations.