When I think of a singularity I think something ?yet to be defined. Like the old map of a spherical object earth. Historically we got a not perfect plane map. Some adjustments needed to be done. This process of mapping the earth to a better map is what I would call the reason for singularities.
It could be a problem of prediction. Its important in generating better objects like a map.
So when facing a singularity you ?assume a new object.