Well, the problem is bad loans were made which means money was created (by the magic of fractional reserve banking) which shouldn't have. Now that money is going out of existence, making a number of companies and people bankrupt. You can allow those bankruptcies to take place and the money to disappear, or you can make good on those commitments by creating cash to back them up.

The second possibility leads to inflation, but it saves the institutions and allows the system to continue to function.

The first possibility would have knock-on effects as one company's bankruptcy immediately impairs assets on everyone else's balance sheet. You could conceivably end up with everyone filing for bankruptcy protection. That would also be a solution: if A owes money to B who owes money to C who owes money to A it can all be netted out to zero but the required disclosures will only take place if A, B, and C are all in bankruptcy court. But it everyone is bankrupt there will be no credit creation and, again, the economy will grind to a halt.

Another way to get the required "circular claims" disclosures to be made is for the government to pull a Roosevelt:

On March 5, 1933, the day after Roosevelt's inauguration, he called a special session of Congress which instituted a mandatory four-day bank holiday. This act provided for the reopening of banks after federal inspectors had declared them to be financially secure.

Just tell people that unless they all sit at a table with the Treasury Secretary and net out their outstanding bad claims, nobody will be allowed to continue in business.

A vivid image of what should exist acts as a surrogate for reality. Pursuit of the image then prevents pursuit of the reality -- John K. Galbraith