We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the "black hole information paradox".)
Here's some reading about black holes singularities and whether they're real or not:
https://www.pbs.org/wgbh/nova/article/are-singularities-real/
https://en.wikipedia.org/wiki/Gravitational_singularity#Interpretation
We know that GR predicts some things extremely well, and QM some things extremely well, but they fundamentally disagree. Both CANNOT be entirely correct, and black holes is the most notable case where one or both break down. (See the "black hole information paradox".)