The devil, in this case, is not in the details; it's fairly easily demonstrable mathematically that if you can travel faster than light by any means, you can violate causality and create an unresolvable paradox. That's the problem with FTL.

Wormholes sidestep this by connecting two locations in space-time rather than two locations in space, which is why current hard SF writers use them. But they're still something of a handwave.