“…but, how is it possible?!”
I have realized that the two wrawls are not equal and in between them lie all possibilities of stories and drama.
A man goes back in time to save himself. You don’t question the time travel, but you question how the man could save himself because that is a paradox.
If time travel were possible, then the paradox could exist. If one paradox could exist, all manner of paradoxes would exist. It’s contradictory, but true, it’s a paradox that does exist. So, if this one does, all should.
Hence, time travel and hence the man saving himself from his future.
Quod erat faciendum. Quod erat demonstrandum.
Taking you from “it’s impossible!” to “…but, how is it possible?” without letting you think that time travel isn’t, is all the craft a good storyteller needs.