The stated reason is often that AIG was so huge that it had to be saved to avoid disaster. Yet, this article seems to argue that the exact reason Lehman wasn't saved 2 days earlier was because it was just too large for the government to handle and that it didn't have the authority to do so until a month later when TARP was passed.
You have to wonder how candid memoirs by former officials are vs attempts to influence the historical record. Wikipedia says that Bernanke now advises Citadel which benefited to the tune of $200 million from the bailout of AIG.