The great american dream gives everyone the opportunity to pursue happiness. And such is the pervading nature of the american dream, that it has become the dream of so many people around the world.
But you live today. While you may have the power to make tomorrow better than today, today remains to be lived.
The pursuit of happiness assumes that happiness is a quantifiable entity, which one can attain, in a binary step. But happiness is a continuous function of various facets of ones life, and incrementally increases or decreases, through the course of your actions.
The pursuit of happiness aims to add an incremental value to the happiness you have in your life. It teaches you to aim for the incremental dx, thereby leaving you to forget the inherent value of the happiness function you may have at that moment.
Thus the paradoxical nature of this pursuit is such, that while you keep toiling away in search for it, you can never find happiness, and when you stop, you realize that it was what was with you all along.