When I looked at S&P 500 PE Ratio chart today, I am surprised that the PE ratio was so high on May 2009, which was 123.73, and it decreased dramatically afterwards. I have no idea why this happened?
Asking why the p/e was so high is best answered "because reported earnings were so low".
Recall that the S&P500 bottomed in early March 2009 when the panic of the financial crisis reached exhaustion.
As noted on the page you have linked, the reported p/e ratios are computed using reported earnings from the trailing twelve months. During those twelve months the banks were writing down all of the bad debt associated with the mortgage backed securities that has lost so much value. This meant that the banks were reporting negative earnings. Since the financial sector is a large part of the S&P500, this alone had an enormous effect on the index p/e. However, the problem was compounded by a general collapse in earnings across the economy as consumers reacted to the resulting uncertainty.
The same site reports earnings for the previous years at $17.11 for the S&P500, compared to $76.17 for the year prior to 2008. That is a collapse of about 78% in earnings. Although the S&P500 has suffered badly during this time, stock market investors being forward looking were starting to price in improved earnings by May 2009. Indeed, the S&P500 was up about 33% in just two months, from its low in March2009 to mid May2009. Thus, by May of 2009 prices were not suffering to the same extent as reported trailing earnings. This would account for the anomalous p/e value reporting in May2009.