https://www.askamathematician.com/2012/07/q-how-does-instant...
http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-ti...
http://www.theculture.org/rich/sharpblue/archives/000089.htm...
The important bit is that it doesn't matter HOW information is transmitted FTL – it can be via wormholes or magic. For observers in another reference frame it will still result in causality violations.
If I got in a faster than light spaceship and traveled to Jupiter, and then turned around and came right back, I would arrive before I left and could shake my own hand on the launchpad.
If we think humans will soon figure out FTL, it makes one wonder why we've not yet seen any human FTL spaceships from the future.
Let's say your spaceship can go to Jupiter in one second (Edit: as measured from Earth), which would require FTL speed. Then you turn around and come back. You've still arrived two seconds after you left.
At Jupiter, you could look through a super-telescope and see yourself still on Earth, but you still aren't really seeing yourself, because you are not still on Earth. You are just seeing the photons you passed during the trip, catching up to you.
FTL enables a kind of time travel that isn't going back in time to shake your own hand. It allows two people in two different reference frames to disagree about whether A caused B or B caused A. You don't get to go "back in time" but you can send somebody lottery results before they're drawn (from somebody's perspective).
That is exactly what it is. You should read the links above to understand what's being claimed.
Now... Please explain to me how communicating through time will allow you to literally, physically, shake your own hand as was claimed.
Why this is effectively time travel is harder to explain without getting into relativity and I'm not going to try right now. The main thing to get though is that you just can't observe events before they happen. It violates causality and if you allow for that (like you totally can with math) then nothing makes any sense and you can't use that math to describe how we know the world to work in any useful way.
Why is that a problem? So let's say I'm on the moon and you're on Earth, and you're watching me through a telescope. I use an FTL cell phone to text you "Hi". Your phone buzzes, you read the message, then visually observe me through the telescope typing the message before you've received it. I guess I just don't understand why that really matters or violates causality. You're just seeing outdated information. There's no way you can interact with my "past" self that you can see through the telescope, it's just a visual artifact.
The explanation for this is complicated, however, so I would suggest you look at the links provided earlier in these comments for a more comprehensive explanation.
The main thing in the situation you're describing is that it's one way. Make it two way, imagine getting a message saying "don't send that message" from someone who has already seen the message you're about to send.
You can imagine this and that's part of the problem understanding the issue I think. But if this combination of events was possible very many things that we know to be true about spacetime would have to not be true.
These are the sort of contradictions that break our understand of causality once you introduce FTL.