Why does the classic 'Square extends Rectangle' design violate the Liskov Substitution Principle?

If Rectangle exposes independent setWidth() and setHeight() methods, a caller can reasonably assume setting one doesn't affect the other. Square, to keep its sides equal, must override both setters so that changing width also changes height and vice versa — which silently breaks that assumption for any code written against Rectangle. A test that creates a Rectangle, sets width to 5 and height to 10, and asserts the area is 50 will fail if it's secretly handed a Square instance, even though Square passes every structural check a Rectangle requires. The deeper lesson is that a real-world "is-a" relationship, which is mathematically true here, doesn't automatically translate into safe behavioral substitutability in code, since substitutability depends on preserved behavior, not just a valid conceptual category.