Which hasn't stopped people from at least trying to figure it out. But even after centuries of effort, "impossible" is more or less the only reasonable answer we have. Maybe someone with a lot of food in their beard might wave their hands about vaguely while muttering something about "wormholes," but even that's not too promising (and again, with the beard and all, that's approaching space wizard terrain).
But Science Fiction Uses It Anyway, Because ...
The whole reason faster-than-light travel was invented for fiction was so that writers could reuse all the old stories they had about sailors and deserted islands and colonies and pirates and just recast them on a galactic scale. Which is kind of the main problem -- the human scale all our existing stories take place in will probably never play nicely with the galactic scale. We're just too small and squishy. In fact, it's kind of ridiculous that we even keep trying. We don't feel the need to tell compelling, character-driven soap operas about what happens when the electron probability densities of two atoms start to overlap, and yet that's not much less realistic than trying to tell the story of a starship captain banging his way across the stars.
A more realistic galactic-scale story, about post-human robot thingies who inch across the stars over millennia, might get around this problem. But it's hard to be sure if post-human robot thingies will be compelling enough characters for our old storytelling tools would work. Can Drone 367834345 feel love? Enough to chase Drone 365742423 through the gates of an airport to tell it how it feels? Will they f**k?
Because I don't have time for a story where they don't.