I think the fear comes from the span of time. If my job is obsolete at the same time as everybody else's, I wouldn't care. I mean, sure, the world is in for a very tough time, but I would be in good company.
The really bad situation is if my entire skill set is made obsolete while the rest of the world keeps going for a decade or two. Or maybe longer, who knows.
I realize I'm coming across quite selfish, but it's just a feeling.