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Because patterns repeat. Barry became the Flash even though his history was altered. On Nazi Earth Oliver still becomes an archer. On Earth 2 Laurel still became a canary.
Barry only became the Flash earlier than he should have in the first divergent reality because Thawne forced it to happen. If not for that he may never have gained powers, or it may have played out naturally.
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We know original timeline Barry went through a crisis event and disappeared. I'm going out on a limb and saying that crisis was averted. But Eobard changed the timeline...now that original Barry doesn't die. So he doesn't sacrifice himself to stop that Crisis. The events that led to that crisis play out but play out at different times because Barry got his powers several years earlier. Barry getting his powers earlier doesn't affect just his timeline...he's had adventures in several timelines (Earth 2, Earth-X, Supergirl earth etc). The Legends of Tomorrow probably wouldn't exist without Eobard's meddling and Barry's indirect influence (Firestorm for instance). So everything they've done in the timeline also all goes back to Eobard and Barry.
Averted? Ah...no. That's the whole point of the Crisis: It's a destructive event that happens across all realities, all parallel/divergent timelines. Infinite universes, but only one event.
And again, the events that lead to the Crisis have absolutely nothing to do with Barry, nor Thawne. Neither were responsible for splitting the universe into a multiverse, neither were responsible for creating the Monitor/Anti-Monitor, and neither were responsible for awakening the Anti-Monitor.
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Eobard's meddling just hasn't affected one timeline's past. Earth 2, Earth X, Supergirl earth in 2019, etc would all be different if Eobard hadn't meddled. Eobard has disrupted the course of events in several timelines which is going to butterfly effect with people zipping back and forth to alternate worlds all the time. Original Barry stopped the original crisis...I think Eobard's actions result in another one that comes earlier. Once that's over the multiverse will die or reset or something and one day a new crisis will happen but it will be in a hypothetical point in time when the Arrowverse shows are already cancelled 
Other timelines wouldn't be affected. For example, time on Earth-1 and Earth-39 seems to be running at the same rate. So Thawne creates the first divergent reality (kills Nora) in 2014 on Earth-1, which corresponds to 2014 on Earth-39.
By 2016 the Earth-1 divergent has been in existence for two years. When Barry pops up on Earth-39 it's just part of the sequence of events that happens there, just like the Flash of Earth-90 turning up there last year. There's no change to the Earth-39 timeline.
