The Fed is a contractor with pomp and circumstance to make it appear different. Any private group charter can require their club leader to be approved by the Pres. and the Pres. may or may not play along.

The Fed is the only entity in existence that can _create_ dollars out of thin air.

US Treasury is responsible for the printed paper dollars, but only the Fed can create "digital" ones.

This is a huge but common misunderstanding.

Every time a bank makes a loan, the dollars are "created out of thin air", and slowly "destroyed" as the loan is repaid.

Parent and GP are using different definitions of "dollar."

GP is using a strict definition (only dollar-denominated liability of the Fed is a "true" dollar), parent is using a looser definition (a dollar-denominated liability of any bank is a dollar).

If you have a fractional reserve (e.g., a bank has $100M cash backing $100M deposits one day, then loans out $30M the next day), with the strict definition you still have $100M dollars ($70M controlled by the bank, $30M that was loaned out and used to purchase stuff). But with the loose definition you have $130M ($30M is still loaned out, depositors are $70M).

Essentially the depositors have made $100M of (debt) investments in the bank, and those investments are now 70% backed by cash and 30% backed by paper (mortgages or other kinds of IOU's from whoever they loaned the $30M to).

That's incorrect. A bank can't give out more dollars than they receive from depositors. It can give out all kinds of paper that is _valued_ in dollars, but not the digital representation of banknotes with the pictures of dead presidents on the front.

In contrast, the Fed can create actual dollars. It can just buy an asset and pay for it with money that it has just created.

When a private bank makes a loan, the dollars are not created out of thin air, no. They loan out depositor's cash.

That is not how things work in the US with banks and loans, they (banks) do actually create "money out of thin air" when they make loans:

https://www.investopedia.com/articles/investing/022416/why-b...

Read the section under the heading: "How Banks Make Loans in the Real World".

creating money in the sense of lending on margin is very different from the sense in which the Fed creates money.

you may have an analogy if your "Any private group charter" was established by an act of Congress, where by the Appointment of the leader was required by law to be done by the president, with the advice and consent of congress

Show me "Any private group charter" that was established by such an act of congress and i will agree with you.

Yes, Congress passed a bill 110 years ago to give a private group broad authorities. The third central bank of the USA.