How do black holes break the laws of physics?

In fact, Newton's laws of motion are a good approximation to General Relativity for relatively slow moving and light objects. A law of physics describes some physical property subject to some constraints. For example, Newton's laws of motion are only valid if objects are not travelling too fast or are not too massive.

General Relativity and Quantum Mechanics are two of the best theories of physics; they both explain a great deal of phenomena, but they are both incomplete because they cannot be combined.

Until evidence was discovered that could only be explained by a black hole, many people did not believe that black holes existed. For example, some stars at the center of our galaxy are traveling at speeds that can only be explained by them orbiting a body around the size of our solar system that weighs 4,000,000 times the mass of the Sun—a description that can only be fulfilled by a supermassive black hole.

The current understanding of a black hole requires the existence of a singularity, which is defined as a point of infinite density and infinite curvature of space time that is beyond the reach of current physics.

The information paradox is the second issue with black holes. According to modern physics, if an object is destroyed by a black hole, all information about its state is lost. Stephen Hawking is developing a theory that suggests the information is somehow encoded in the event horizon, which could potentially resolve this issue.

So, the singularity and the information paradox are two ways in which black holes violate known laws of physics.

The behavior of matter at infinite density (singularity) and the nature of spacetime near the event horizon are examples of extreme conditions where our current understanding of physics is pushed to its limits. Black holes, however, do not break the laws of physics. Rather, they are a consequence of the laws of physics, particularly general relativity.