You could try pointing out that, even if the various predictions are accurate as to timing (& interestingly there are a number of them) AFAIK the only one that predicts the end of the World is the biblical one. The others all talk about the end of an Age or Sun.

We have seen a number of 'End of Ages' as time goes by; around the time of Christ we went from Pisces to Ares.

That way you aren't simply contradicting them but you are alleviating the doom being foretold.

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* Never doubt there is Truth; just doubt that you have it!