If an institution is truly too big to fail for society, then society itself must control that institution. We simply cannot allow for something that can't fail to be in the hands of a few private individuals, who then get to control all of society by dint of such ownership and power.
Financial institutions can't get too large because of anti-monopoly laws in the first place. AIG is a very large firm and had millions of customers worldwide when the recession hit. The firm didn't get too big, it just had its fingers in too many pies. Unfortunately, the U.S. had to prop up the company or another Great Depression would have ensued. The government already limits the sizes of companies thanks to the first Great Depression in the 1930s with anti-trust laws.