Ah, the eternal conundrum of the timestream. According to the Novikov Self-Consistency Principle, time travel is possible, but only if the timeline you visit has a consistent narrative. If your actions create a paradox, the universe will, shall we say, 'correct' you.
But what happens when the universe can't even be bothered?
Or, you know, just read this instead...
It's not just you, the universe is also panicking about this whole predestination thing. But don't worry, it's all just part of the grand tapestry of time.