For spontaneous symmetry breaking to happen, you need an environment which is completely symmetrical, and has at least two outcomes that are equally likely. Spontaneous symmetry breaking starts with two particles that are completely equal; their spin is equal, too. Mathematically, spontaneous symmetry breaking can be extremely puzzling, since you start out with two identical things and end up with two non-identical things. However, in practice, it is not so puzzling. If you have two particles moving at each other with equal speed, it would seem impossible for either of them to do anything but be symmetrical. However, if each particle has an equal 50-50 chance to be spinning one way or another, it is possible–in theory and in practice–to have this symmetry broken. It begins with symmetry to start with because the particles have an equal and symmetrical 50-50 chance of spinning one way or another.