I guess I explained how the got so many mating types without even touching the reason why. And to be honest I have not really read anything about why they have this complex system. However, my first thought would be that they do not use the sex in a strict way like we do. For them it does not matter which mating type they create an offspring with, and that the mating types instead act as a regulator to prevent it from mating with the exact same type (so it will not fertilize another part of itself).