Again, if the White House were to be the primary target of a nuclear strike, you can likely count on the rest of D.C. going down with it. That includes the Pentagon. But leaving the Pentagon out of it for a minute, a strike on the White House would destroy the executive branch of the government (the president, etc.), leaving the country leaderless and rudderless for some time. It’s easy to see why it would be a primary target for a hostile government.
Next: Recalibrate those missiles to hit a bit further up the East Coast.