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The end of Ep 20 is probably a sequence reshuffle. Timeline-wise, the Tonkii and Asuna parts can happen more or less at the same time so I don't see the issue here - all that really needs to happen is for Asuna to get the keycard before Kirito makes it to the world tree.
Also, I think there are tons of complaints about Asuna being a damsel in distress all over the place, so it's likely a director's imperative to break up Kirito's OPness with some Asuna.
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