It seems like you're missing a key concept here: "simultaneous" depends on reference frame. If two events separated in space, A and B, happen at the same time in my reference frame, there's a reference frame in which A happens before B, and a reference frame in which B happens before A. There's no one true order of events.
This causes no paradoxes in relativity, precisely because you can't send information, or cause an action, faster than the speed of light. The propagation delay between A and B ensures cause precedes effect in every reference frame, and the order of events can't quite shift enough to overcome that propagation delay.
But moving FTL breaks all that. If I move "instantly" in my reference frame, then there's a frame in which I move back in time, and a frame in which I jump forward in time. I don't move back in time in my own reference frame, sure, but I really do in another. And if you're moving quickly relative to me, I can use that to relay a message from you to your past self - either by a series of accelerations between the frames, or by using a friend in your reference frame who can teleport as well.
If I want to visit my own past self, I would need to teleport some significant distance, accelerate up to relativistic speed, again teleport a significant distance, then accelerate again to match location and speed with my former self - elaborate, but possible. Or, if I could travel a great distance, say 1 billion light years, "instantly", then I don't need much acceleration at all, just the difference in velocity the Earth achieves in 6 months as it makes half an orbit would do it.