A simplified explanation of why you can't travel through space faster than the speed of light is that you are already traveling at the speed of light, through spacetime.
If you are stationary in space, you are traveling at c in time. If you speed up to c in space, time appears to be stopped and you are not traveling in time.
To travel backward in time, you'd want to go faster than c in space, so that time will be forced to be negative.
By my logic, that means that you have to also be able to do the opposite, travel back in space. Except, if you slow down to 0 and the keep accelerating, you'll just be traveling forward in the opposite direction.
Is this line of reasoning correct? How would time travel be possible considering this? I'm not talking about alternate universes and similar things that are time travel in name only.