Consider the following problem, called BoxDepth:
Given a set of $n$ axis-aligned rectangles in the plane, how big is the largest subset of these rectangles that contain a common point?
Say we proved these two statements:
There is a a polynomial-time reduction from BoxDepth to MaxClique.
There is a polynomial-time algorithm for BoxDepth with $O(n^3)$ runtime.
Why don’t these two results imply that P=NP?