A lot of companies outsource their customer service call centers, why do you think they do so?

Customer Service call center should not be outsourced as it is the competitive advantage the one firm have over the industry. It gain the unique selling preposition if maintained and provided effectively

Cost savings. :) especially they are looking also for countries who is good in this, less time to be trained and more time in production.

The only reason is cost saving.

Primary reason is cost efficiency, also time zone advantage. most organizations who opt for outsource call centers are multinational and has market reach in many countries. another reason could be of language reach. all the above reasons make the operation more efficient and larger market reach. 

The main reason on why some of the companies outsourced their call centers its because of cost saving. We all know that putting up a call center companies requires lots of money by getting staff, for the equipments and for the trainings, but if you will outsource you will only pay for the services of the agents per hour and per leads sometimes, and most of the time in house staff agents are only trained for specific accounts but outsource agents are trained to handle multiple accounts to gain more clients and they are flexible.