This is a good explanation, I've had to explain this topic a few times as well, it seems like it's one of those topics that is very missunderstood.

To just expand a bit, I believe some of the confusion around printing of money comes from the way some economics reports are built. As a micro example, Assume a 10% required reserve, If Alice deposits $100 and the bank lends $90 to Bob. Alice ($100 deposits) + Bob ($90 cash) think they have $190 in total.

This is mainly useful for economists to understand, study, and report on. However, when the reports get distributed to the public, it looks like the banks printed their own money, as we now see $190 on the report when there is only $100 of cash in our example system.

Whether the system should work on a fractional reserve is it's own debate, but we need to know what it is to debate the merits and risks of the system.