I haven't seen any very clear explanation of why FTL implies time travel on this thread yet. I'm not a physicist, nor do I play one on TV, but I think I finally understand this point, after reading Forward's Timemaster. Real physicists are invited to correct me if necessary, but here's how I think it works, really short and sweet.

Lets imagine a spaceship travelling STL, but close to c, away from Earth. Due to 'time dilation' the observers on Earth say time has 'slowed down' for the travellers; say when 2 years have passed on earth since launch, only one year has passed on the spaceship.

For the travellers, the situation is exactly reversed; they see Earth as having 'slowed' time, in exactly the same ratio.

Now suppose the Earthlings fire up their ansible and send a message to the ship after two years have passed. This sends messages simultaneously, with respect to Earth. Due to time slowing down, the ship receives the message after only one ship-year has passed, since one ship-year equals two Earth-years, from Earth's point of view.

Now the ship decides to reply, and fires up their ansible, which sends messages simultaneously from the ship's point of view. According to the ship, one ship-year has passed, but only 1/2 Earth-year has passed, from the ships point of view. So their simultaneous reply gets to Earth after only six months have passed on Earth. The reply is received 18 months before the message was sent. That is a true violation of causality, and will appear to be one to all observers.