Earlier quoted context omitted.
This is exactly right given our current understanding of the universe. FTL travel violates causality, which is a fundamental principle of the universe. I wouldn't go quite so far as to say it's totally impossible though. There is a whole lot about the universe we don't understand and I can't rule out the possibility that there are entire branches of mathematics and physics that we don't know about.
Can you or someone else "explain to me like I'm five" why faster-than-light travel violates causality?
Imagine a friend and you, moving very fast with respect to each other. You measure your friend's clock as advancing slowly (due to time dilation), on account of the fact that he's moving with respect to you. But your friend measures _your_ clock as advancing more slowly than _his_, because motion is relative.
The way to reconcile this mathematically is to give up on absolute simultaneity of distant events. In other words, when two things happen in different places, at the same time according to your clock, they happened at different times according to your friend's clock. This is analogous to how you measure your friend to be in different places in different times (because he's moving with respect to you), but he measures himself to be stationary, always in the same place. To recap: If comparing things at different moments, "being in the same position or not" is relative to the observer. If comparing things at different places, "happening at the same time or not" is relative to the observer.
That's how causality comes in. If your friend tosses a very fast ball at you, and the moment you receive the ball you start towards him faster-than-c, you'll arrive where he is before he tossed it (if you went fast enough). That's what the equations say. Now the breaking of absolute simultaneity allows naturally for disagreements on what of two things happened first, assuming they happened far enough from each other that light couldn't cover the distance in time. But by putting faster-than-c velocities in the equations, we have your friend and you disagreeing on what happened first (him tossing the ball, or you arriving where he is?) in what (to him) is the same place. And it's not just a confusion of the mind: all your measuring and recording artifacts will agree with you, and all of his will agree with him. The mathematical conclusion is that if you can send information faster-than-c, you can send it back in time and break causality.