There are three possibilities.
First, Petraeus and other CIA officials had absorbed too much of the speculation on Twitter, and on the website of the U.S. Embassy in Egypt, pinpointing an anti-Muslim YouTube video as the cause of demonstrations in Cairo on Sept. 11, 2012. It’s also likely that officials in Langley received lots of intelligence reports — after the attack — that reinforced the view that Cairo’s heat sparked Benghazi’s fire.
The intelligence from the agency’s clandestine service, through its own sources and foreign liaison channels, has a way of highlighting the wisdom du jour. This isn’t tendentious; it’s just the way human nature plays out in the intelligence business. Cairo’s frenzy just bled into Washington’s analysis of Libya.
A second possibility is that Petraeus pre-empted his analysis because he knew Obama would be happier with the YouTube narrative than with the truth that an al-Qaeda affiliate had planned the attack, which killed U.S. Ambassador J. Christopher Stevens and three other Americans. This shading can happen subtly in the executive branch, to the extent that officials aren’t conscious that they are doing it. This is “group think,” and it’s hardly unique to the CIA.
The third possibility is a combination of the first and second explanations.