Do black holes defy the laws of physics?
Nothing should be able to defy the laws of physics. If something is inconsistent with the laws of physics then they need to be modified to accommodate the inconsistency.
Black holes are extreme objects. They were predicted from the Schwarzschild solution to Einstein's General Theory of Relativity. Many people didn't think that they existed until evidence was found. A black hole could explain the galactic X-ray source at Cygnus X-1. It is now believed that most large galaxies have a supermassive black hole at their centres.
One issue with black holes is that the theories suggest that there is a singularity inside them. A singularity is a point of infinite density and infinite curvature of spacetime. The physicist Kip Thorne described the singularity as the point where all laws of physics break down.
Another problem with black holes is the black hole information paradox. The issue is that if a particle falls into a black hole information about its state is lost. This is forbidden by the laws of physics as we know them. Stephen Hawking is working on a new theory by which the information is somehow retained at the event horizon.
Clearly we need new laws of physics if we are to completely understand black holes. As nothing which goes past the event horizon can ever escape. This makes it impossible to see inside a black hole.
So, yes, black holes defy the laws of physics as we know them. This means that our laws of physics are incomplete.