Q. Why are there Four Math-habs?
A. In a nut shell, the four Math-habs are the products of the Sunnah of Rasulullah (sallallahu alayhi wasallam). The Sahaabah who had spread out in the different parts of the world after the demise of Rasulullah (sallallahu alayhi wasallam) taught Islam the way they had seen Rasulullah (sallallahu alayhi wasallam) practising and teaching it. Rasulullah (sallallahu alayhi wasallam), for example, performed Salaat in different ways. Those Sahaabah who saw one way, went away and taught it the way they saw it.
Then there are certain Ahaadith which Rasulullah (sallallahu alayhi wasallam) did not fully explain. But he instructed the Sahaabah to deliver everything they heard from him because there will be such people who will understand the Hadith better than its carrier. The carrier refers to the Sahaabi narrating the Hadith, and the others who would interpret it refer to the Aimmah-e-Mujtahideen during the age of the Taabieen.
This is a brief background to the Math-habs. Whilst in the initial era of Islam there were more than a dozen Math-habs, today only the Four Math-habs comprising the Ahlus Sunnah remain.