2) The compounding nature of interest pushes a quasi-exponential growth of the debt/credit. Since the credit participates as an effective part of the money supply, it produces inflation. When the growth of the debt becomes unsustainable, a process of liquidation (shrinking credit) begins, which causes deflation, which accelerates the liquidation in a positive feedback. The liquidation periods are known as recessions or depressions.
This is the one I was probing for, since I hear it occasionally, and it doesn't seem valid to me.
If you play around with toy model closed economies of only a few participants, you can create all kinds of scenarios where the base money supply is constant, and there is prolonged, stable lending going on between participants, without the need for any inevitable bankruptcies. I.e. you can come up with counterexamples to your assumption that "the compounding nature of interest pushes a quasi-exponential growth of the debt/credit."
Yes, you can create such examples. If the profits are greater than the interests, the debt doesn't have to grow. But when there's losses, someone will eventually buy the failing business with its debts. Well, or it can go bankrupt. It is hard to prove.
Just think this. If a single family would have saved an ounce of gold and lent it with 5% compounding interest (the father gives the gains to the son, etc) since the year 0, their wealth would be right now 4.08959621 * (10 ^ 42) ounces = 1.15938102 * (10 ^ 41) kilograms.
The total mass of the earth is 5.9742 * (10 ^ 24) kilograms.
So their wealth would be (1.15938102 * (10^41)) / (5.9742 * (10^24)) = 1.94064648 * (10 ^ 16) times the total mass of the earth in gold. Obviously there's not that quantity of gold, so their compounding loan would be eventually unsustainable. Note that the borrowers could have payed back their loans and then the family lent to other people, but the total level of debt to the family would be always increasing.