Roughly speaking, the system has stable configurations where the free magnetic energy $W_{\rm mag}$ assumes a strict local minimum.
That local minimum of $W_{\rm mag}$ is assumed where the combined permeance of the magnet and the iron plate has a strict local maximum.
Symmetry, is not always a valid argument in this regard. E.g., assume a circular iron ring with a hole that is larger than the magnet. Then the central position of the magnet (i.e., magnet in hole) will not be a local maximum of combined permeance. It will be a local minimum. That means the central configuration will be an equilibrium, but an unstable one.
Pityingly, this description is rather rough since it works with concentrated parameters like permeance and the problem actually has distributed parameters.