Space is the absence of matter. Space is nothing at all. Therefore, outer space doesn't exist. If it's not there, how can you fly through it?
But seriously, people talk about faster than light space travel by means of bending or warping space (as in Warp speed). That would be like a bedbug traveling quickly from one corner of a bed to the opposite by folding the sheet bringing the bug’s destination just a hop away from its current location.
The problem is that space is nothing. There is no “fabric of space”. How can you bend or fold nothing? Furthermore, how could a relatively tiny spacecraft pull two parts of outer space together? We've no better chance of that than the bedbug does of folding a sheet. I would also point out that space is not a flat sheet, but rather an infinite ball in all directions. How can you put a bend anywhere inside of a ball?
One more thing. To make even a tiny wrinkle in the “fabric of space” you would have to pull an infinity of space from one direction and push out against an infinity of space into an arc of several directions simultaneously.
And yes, space is infinitely infinite. If you could travel through space at a trillion times the speed of light, you could pass millions of galaxies and never run out. Even if there is a limit to the number of galaxies and you've passed the furthest most galaxy in the universe, you could still travel through empty space for all eternity and never reach any kind of limit. The allegory of a sphere doesn't really work either because that is a shape with an outer limit, but infinity, having no limits, can't have a shape.
I'm not saying that light speed or beyond can never be achieved. I'm just saying that it can't be achieved by the disfiguration or manipulation of space (nothingness) itself.
Now, if you can wrap your head around all that, your mind is seriously warped.