Explained here. Excerpt:
Let’s say that Citigroup were restructured – via bankruptcy, or via
government conservatorship – in such a way that creditors did not get
all their money back. (None of this applies to FDIC-insured deposits or
to recently-issued senior debt that is explicitly guaranteed by the
government.) They might be forced to convert debt for equity, or they
might be stiffed altogether. The first-order concern is that this would
have ripple effects that could take down other financial institutions.
According to Martin Wolf,
bank bonds comprise one quarter of all U.S. investment-grade corporate
bonds; losses would be spread far and wide, hitting other banks,
pension funds, insurance companies, hedge funds, and so on. If
Citigroup did not support its derivatives positions, then institutions
that bought credit default swap protection from Citi would face further
losses. (I believe that most U.S. banks were net buyers of CDS
protection, however.) The fear is that it will be impossible to predict
how these losses will be distributed and who else might go down.
The second-order concern is bigger. After all, Lehman did not seem
to force any major financial institution into bankruptcy, although it
may have twisted the knife that AIG had already stuck in itself. Once
investors figure out that bank debt is not safe, they will refuse to
lend to any banks, and we are back in September all over again. Or
almost: it is possible that the Federal Reserve’s massive efforts to
provide liquidity to the banking system will be enough to keep banks
functioning. But who wants to take that risk?
You're comparing that to spending a great deal of extra money on credit bail-outs; choose your poison.