Originally posted by Nephthys
Remember that Thawne tried to go back to kill Barry as a child, which would cause the same paradox since then he'd never have fought the Flash at all and had no reason to go back to kill him.
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Same thing happened in Looper. Actually almost exactly the same thing happened as the Flash finale in Looper.
You can't really do time travel stories if it leads to a paradox every time. The changes made in the past have to stick, no matter what the repercussions are for characters from the future.