However, things start to change once we get closer to the year 2000, and a lot of these movies seem to become more political in nature. The Rock actually gives its villains an understandable (if poorly explained) goal in the form of making a statement about how the government has treated the families of fallen soldiers. Air Force One is notable for bringing in actual terrorists as the villains for once. Instead of being after money or some other petty goal, the antagonists actually have a political end goal in that they are trying to free a brutal dictator in whose capture the President had a hand.
Air Force One and The Rock therefore take a much stranger turn in that they begin to turn patriotic in nature (or at least attempt to, in the case of The Rock). Air Force One helps to enforce the shift in tone by making the central character the President himself, and casting him as an action hero who has to save the day. This gives the film added stakes in that there is a sense of having to save the country instead of simply stopping the terrorists and saving the hostages. It is also worth noting that around the same time the movie Independence Day was released and made famous by its scene depicting the destruction of the White House.
Hollywood seems to enjoy finding ways to blow up the White House, seeing as it has done it several times since. The "Die Hard on an X" formula began to lose its popularity around the same time, but it never truly went away. Die Hard imitators were still made, and they still happen today, just not as frequently much like how there people continue to make film noir and slashers long after the height of their popularity. Movies like Panic Room, Red Eye, and Dredd all have elements of the "Die Hard on an X" formula, with Non-Stop possibly being yet another "Die Hard on a plane" movie. Possibly the most curious development happened in 2013, which saw the release of not one, but two action films that functioned as "Die Hard in the White House".
Olympus Has Fallen and White House Down came out only a few months apart from each other. Plot-wise they were quite similar, using elements of the "Die Hard on an X" formula to tell the story of a man associated with the Secret Service (a troubled agent in Olympus Has Fallen, and a rejected applicant in White House Down) who proves himself when he becomes the only hope after the White House gets overrun by terrorists. Chaos inevitably ensues at the expense of the White House. Olympus Has Fallen is definitely the better film of the two (though White House Down had some interesting ideas) but there is something to be said about the fact that there were two "Die Hard in the White House" movies released the exact same year.
Both films made a spectacle of demolishing the building (though perhaps not on quite the same scale as the famous scene from Independence Day. While it is normal for the "Die Hard on an X" formula to prominently feature the gradual destruction of whatever location serves as the setting, be it a shopping mall (Die Hard), a boat (Under Siege), an airplane (Passenger 57, Con Air, Air Force One), a bus (Speed), or Alcatraz (The Rock), Hollywood seems to have a disturbing obsession with the White House in particular.
The big question is why American films have such a strange love for blowing up their own government buildings, and why the White House in particular? You don't see very many Hollywood pictures that make a display of destroying say... the Canadian Parliament buildings or Buckingham Palace. The answer likely lies in the sense of patriotism that, ironically, is often a crucial part of American movies that feature the destruction of the White House, but why the White House in particular? After all, the American government has plenty of other significant buildings. Why not blow up the Pentagon, for instance?
While the American Government has a wide variety of important buildings, the White House is probably the best known, and is often seen as a figurehead of sorts. That view might not be entirely unjustified either, seeing as it does serve as the home of the President and his family (and indeed it is also the site of many government operations). When discussing American politics with anybody, American or otherwise, more people are likely to think of the White House than the Pentagon or the J. Edgar Hoover building. Because it is such an iconic landmark in the American political scene, it is easily recognizable to most viewers, even people (like me) who aren't actually American.
The fact that the White House is such a well-known image therefore makes it one that will stand out more in the viewer's mind, and a perfect candidate for destruction. If you blew up the Pentagon you might still make an impact but it would not have quite the same impact. By destroying the White House, the home of the President and essentially a figurehead for the entire American Government, you depict the fall of American power. The destruction of the White House in Independence Day, Olympus Has Fallen, and White House Down all symbolize the danger that is posed to the American people, something so great that even the President is at a loss on how to deal with the situation.
However, it is also worth noting that the President himself (he is usually a man) often survives the destruction of his home and tries to fight back. In Air Force One, the President literally becomes the only person who can stop the terrorists who have hijacked his plane. In the cases of Independence Day and White House Down, he manages to barely survive the destruction of the White House and ultimately has to rally together his remaining allies to save the day. In essence, the destruction of the White House symbolizes the President's loss of power and sets in motion his quest to earn it back.
The one exception to the rule is in Olympus Has Fallen, in which the President spends most of the movie imprisoned by the terrorists, and it falls upon a disgraced Secret Service agent to rescue him. Instead of the President reclaiming his power, the journey becomes about a man's quest for redemption by serving his country. While it is not the President himself, the destruction of the White House still serves a similar purpose, as he is rendered powerless and left at their mercy when the terrorists trap him in his own bunker. In the end, The hero regains his honor by saving the President and essentially restoring him to power.
Ultimately, destroying the White House presents an ironic message. Because it is such an iconic figurehead of American politics, destroying the White House takes away the President's authority and forces him to earn it back. Blowing up such an important landmark therefore creates a paradoxically patriotic message by depicting America as a nation that will not go down easily, and no matter what trouble arises they will always find a way to come out on top once again. Putting it simply, the reason why so many American films like to demolish the White House is, strangely enough, to enforce the image of America as a dominant power.