Anxiety is a perverse thing. Those with it who have any measure of self-awareness soon learn to recognize its almost capricious irrationality, though, and cope with it. Afraid of X, that looming future event? Just wait until it's almost upon you, or you're in the thick of it. While you're engaged in X you'll be completely distracted from your fear of X because of Y, which is just around the corner. It almost seems like some people have a default setting of 'being afraid of an imminent event approximately one week hence.
With a little forethought, of course, it's not difficult to manipulate the situation to prevent it from interfering with daily life. Much anxiety is simply a fear of novelty, and throwing yourself into the situation repeatedly will eventually breed contempt for it. Also, there's really nothing that'll overcome your fear of flying quite so much as utter preoccupation with what you'll have to deal with when you land. Any pessimist's instinctual knowledge of our own fate (in all its profound myopia) tells that us that it would simply be too convenient to perish before undertaking some vile or tedious chore.
I imagine that evolutionary psychologists -- those trustees of the Freudian tradition of ad hoc accounts -- have some explanation of how anxiety evolved and what it was originally good for. And the existentialists, among others, doubtless have their own a priori account. But it seems to me to be an imminently human trait to co-opt the things we discover in the world for new and unexpected purposes-- including co-opting our own emotions and reactions to things to make them better suit our purposes. Our reflexes are more malleable than we may assume.