I figure at least some of it comes from the idea that mathematically, a singularity is a point (e.g., in the graph of z=1/w, there is a singularity at the point w=0, and in the graph of z=(1-w)²/(1-w) there is a removable singularity at w=1 (that is, the function is undefined at w=1, but if you put a point at (1,0), the graph will be continuous and no longer have any holes in it). The fact that both have the same name and the similar behavior of a black hole singularity to a mathematical singularity¹ can lead people to make an incorrect assumption.

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1. I must admit to a lack of sufficient GR education to feel confident in this, but I think that one of the issues that made physicists unwilling to accept the idea of black holes when they were first postulated was that there ended up being a division by zero in the mathematics.

As someone with basically only popsci knowledge of black holes: people claiming it would be a literal point never made much sense - fundamentally, common sense (as much as it can apply here) dictates that you cannot compress particles to an absolute point.

Or read Susskind's "The Theoretical Minimum: General Relativity". For a non-spinning blackhole at least, not only is the singularity not a point, it is a surface in time, not space (as the book explains, the space and time coordinates switch places as you cross the event horizon).

I think it's not even a valid critique of that and it's sort of playing games with what the definition of a singularity is to reach the claim that it's making. I think the topology of the singularity is not even a well defined question and certainly not well understood enough to bear the strong claims in the paper.

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