In general relativity a black hole actually has zero volume and thus infinite density. If it has angular momentum it will collapse down to a ring of zero thickn

In general relativity a black hole actually has zero volume and thus infinite density. If it has angular momentum it will collapse down to a ring of zero thickness and finite radius less than the Schwarzschild radius. So basically the assumption for the singularity is because the mathematics of general relativity leads to (coordinate independent) divergence at the center of the black hole. What the physical significance of that is and how it jives with our understanding of quantum mechanics isn't fully understood.