Symmetry breaking is the general phenomenon that underlies most of that.
The classic example is this:
Imagine you have a perfectly symmetrical sombrero[1], and there's a ball balanced on top of the middle of the hat. There's no preferred direction it should fall in, but it's _unstable_. Any perturbation will make it roll down hill and come to rest in a stable configuration on the brim of the hat. The symmetry of the original configuration is now broken, but it's stable.
1: https://m.media-amazon.com/images/I/61M0LFKjI9L.__AC_SX300_S...