They fly amazingly close to the Whitehouse yet bypass it only to pull off an incredibly difficult 270-degree maneuver to hit the Pentagon. In an area that is under construction. While pulling off that maneuver the aircraft would have been vulnerable to retaliation from air defense missile batteries on the ground. Doesn't the Pentagon have such defenses? Or did I hear that they were dismantled previous to 9/11/01?
Anyway, why hit the Pentagon? The Whitehouse makes a much better target of opportunity. Hitting the Whitehouse makes much more sense symbolically even if you inflict less or no casualties(excepting the onboard passengers). One might say that this is proof the Flight 93 was going to hit the Whitehouse and the terrorists were merely "on task". I disagree, in a "hodge-podge" operation such as this, a terrorist attack where there are several independent entities acting in concert yet unable to communicate with one another, each team goes for the biggest "prize". Once that target has been eliminated then subsequent teams move on to other various targets.
The Whitehouse or the U.S. Capitol are much better targets yet they chose a target that is less important, the Pentagon. Plus there are various better targets of opportunity within blocks of the Whitehouse: the U.S. Capitol, the World Bank, the IMF, the Watergate Complex or the State Department.
So why the Pentagon? The planners(PNACers, Cheney) needed the outward appearance of multiple targets and multiple threats. With the concentration of the destruction happening in New York they needed to create the appearance that the nation's capital was also under attack. But they didn't want to actually destroy any buildings in the process. The Pentagon is that target as a direct hit to the Whitehouse would likely destroy the entire complex. Plus it provides them with deniability, who would dare attack themselves or blow up their own buildings?