Okay, I'm going to try and clarify why this stuff breaks causality. In short, it is due to the effects of relative simultaneity, as a few other posters have tried to explain. In short, there is no such thing as a universal "present time". Time is flowing differently for all objects based on how fast they are moving and in what direction they are moving.
To illustrate this, I will use an example I will call "relativistic air traffic control". Imagine that there are two base stations in the same frame of reference, but several light-years apart. Let's call these stations A and B. Now, imagine that there is also a spacecraft flying between A and B, called craft C. Spacecraft C is travelling at a significant fraction of the speed of light from A towards B. All three of these have imaginary FTL communication systems that let them communicate simultaneously with each other.
Now, let's imagine a simple message transfer. Station B sees the incoming spaceship C, and sends a message to station A requesting info on it. Now, from the perspective of the two base-tations, the transmission and reception of the information is instantaneous. However, from the perspective of craft C, station B will send the request first, and station A will receive the reply later. Note, this is not an illusion or anything, space-time just works differently for the different frames of reference.
Now, station A then sends an automated request to spaceship C to send a message to base station B. Craft C automatically complies, and relays the information to ground station B. The result? Due to the differences in what "simultaneous" means between the frames of reference, a simple relayed message has a time-delay introduced into it, one that can send the message either forwards or backwards in time from the perspective of the ground stations.
If you were to introduce a second spaceship moving in the opposite direction, things become even more confusing, since it will see transmissions between A and B happen in the opposite order that craft C does. Bounce enough messages around between these stations and craft, and you can send messages years into the past. Causality will completely break down thanks to simple air traffic control and communication relaying.
That's why FTL communication doesn't work with our knowledge of the laws of physics. Space-time just doesn't work the way people are accustomed to.