One is what initially motivates people to predict apocalypses. I think there are many motivations. They variously include, in no particular order: a desire to see other people get their comeuppance; some sort of assumptions about the nature of life (e.g., that God will destroy all injustice or that mass violence is the inevitable consequence of human striving); a propensity to believe engaging stories compellingly told; the existence of actual grave dangers; and the excitement of knowing something other people don't. (I'm not sure if you had in mind the first of those, the last of them, or something else.)
Once people expect apocalypses, it's often hard to get them to abandon the expectation -- and that may have something to do with wanting to prove that they are right. It doesn't seem to me that just wanting to be proven right is much incentive for apocalypse in particular, unless it's "right" as in "one of the elect."