The problem is that AIG underwrote a lot of contracts that were then used to cover leveraged positions, etc. It's turtles all the way down and AIG is somewhere down at the bottom of the pile. In addition to the load of mortgage debt it dabbled in it played a role writing insurance for a massive shitpile of financial instruments; if the underwriter declares bankruptcy then a lot of things need to be unwound in a hurry. This is a huge problem, and would have a far greater impact than letting some retail bank fail. While other companies could fill the void, they could not do so quickly. The speed that is required here is the problem (e.g. when LTCM went tits-up it had the good grace to do so on a Friday so that deals could be struck over the weekend.)

As far as Sweden's banks go, I think you should check again. They have losses in US mortgages (it wasn't just US and Chinese banks buying those securities) to cover and are also feeling the heat on over-exposure to Baltic loans that are starting to go sour. The Swedish bank takeover was somewhat akin to the US S&L takeover in the 80s, except in the US case it did not eat 4-5% of GDP...

"If there's a need (market), new companies would have sprouted up."

You aren't even addressing the given reasoning for the bailouts. Meaningless platitudes don't solve problems.

I don't think he/she has to address the reasoning for the bailouts, or that he/she used meaningless platitudes. He/she even cited an example.

You don't have to address the other sides reasoning because it's hard to find every flaw in an opponent's argument.

If you ignore the the actual reasons why the bailouts happened, how can you argue against them? Sure, the bailouts preserved weak companies, which is a bad thing, but you can't just ignore the benefits of the bailouts and say they shouldn't have happened. That in no way resembles an argument, though "meaningless platitudes" may have been an incorrect characterization.

"You don't have to address the other sides reasoning because it's hard to find every flaw in an opponent's argument."

But the other side has put out a public statement explaining their actions. This isn't about predicting how someone is going to make their case. The case has already been made. At the very least, you have to address their justifications.

What about the example of Swedish banks that failed and were not bailed out? Surely that serves as a counter-example.

The goal of the bailouts is to minimize the effects of bank failures on the economy, not to make sure the banking system is sound in the future. The counterexample isn't valid. A valid counterexample would involve a country avoiding a recession while not bailing out failing banks, but even then, I don't think this particular situation has a historical precedent similar enough to be pertinent.

Also, after actually looking into the example, it looks like Sweden did bail out the banks to end the crisis: "The government rescued the banking system by issuing a general guarantee of bank obligations. The total direct cost to the taxpayer of the salvage has been estimated at around 2 per cent of GDP." (http://ideas.repec.org/a/oup/oxford/v15y1999i3p80-97.html)

Even with a valid counterexample, I think you should still have to explain why the current course of action is wrong, not just why another would be right, which is why I didn't address it in the first place.