[ars]

You are confused because phase transition is not a good description of symmetry breaking (sorry cohomologo).

You have to understand that there already is a difference between the two things (forces, particles, whatever). It's just in certain temperatures or forces, or size ranges (whatever) that broken symmetry is not visible and the two appear to be identical.

So the search is on to understand why these two things should act so identically in certain ways, and yet not identically in other ways, i.e. what breaks their symmetry.

Finding out what breaks their symmetry tells you a LOT about the particle, it tells you what is identical, and what is different.

For example an up and down quark are identical in all ways - except mass and charge. So in certain experiments they appear identical, in others those things show up - their symmetry is broken.

But noticing that they are identical in certain situations tells you a lot about quarks, and noticing where they differ tells you even more.