The monetary system is based upon units of account which are mostly created via debt instruments. So the interest on debt is always greater than the total supply of money units. Therefore, the debt is mathematically impossible to settle.
It's not mathematically impossible to pay back all debts. The interest doesn't vanish, the banks use it to pay their expenses and shareholders. Indirectly the money can flow back to the indebted, which can then continue to pay back.
Since debt is the main mechanism of monetary creation, paying it all back would result in massive deflation, so it's not practical unless money is created in another way to compensate, or another currency replaces the dying one.
Strawman: My premises did not say "debts can't be settled all at once". My premise said "the [total] debt is mathematically impossible to settle." Nowhere there does it say "all at once" though that is true I agree its not relevant.
But some debts can never be repaid except by default or replacing with another debt. So insolvency is hidden and total debt gets bigger. Then insolvency is exposed. Then bailouts are required to kick start a new round. Eventually bailouts are no longer tolerated and the system collapses.
"what matters is that each debt can be paid back in due time" is irrelevant because "each" implies non-systemic. And my premise is in the systemic context (i.e. from original argument "economic system is heading towards collapse"). What matters is that total debt of the system grows and grows.
It's a fairy tale to assume that the quantity of debt and its continuing growth is "irrelevant" or "perfectly normal" to a healthy financial system. The global financial crises of 2008, Greece 2015 and the history of nations defaulting on debt reveal this truth.
It's quite normal for a monetary mass to grow, for money to be created faster than it is destroyed. Currently debt is the main mechanism of monetary creation, so it's normal for debt to be created faster than it is paid back. You should worry when it doesn't, that indicates deflation.