Against rigidity in composition.
The rule of thirds suggests that a well-composed photograph has a key point of interest at one intersection of an imaginary tic-tac-toe grid superimposed on our image. The general idea is that symmetry is boring, the eye delights in seeing some dynamic weighting in an image, and that by making one of these four points our “focus” we have created an optimal balance.
This isn’t a bad idea for beginners, but it can only be a rough guide to help teach and demonstrate composition. But once absorbed, it should be discarded as too mechanical an approach. Of course composition likes some sense of balance and offset, but the best artistic compositions are done by feel rather than formula.