You got it in the third sentence and then dismissed it for some reason?

That's exactly what the Singularity is: it's the transition point beyond which meaningful predictions aren't possible.

In a black hole it's the center where relativity breaks down.

In AI it's the point at which non-human intelligence no longer requires human intelligence for self improvement: after which predictions of the future become somewhat meaningless.

In the human lives experience, I would argue its like having your first child: you can know what's coming, study the theory, know everything to expect and youre still you on the other side...but you can't really know what will happen till you get there.