Why consider offshore / business process outsourcing (BPO) to India?

Business Process / Offshore outsourcing has been popular for several years. Countries like India are popular offshore outsourcing locations which offer cost effective solutions. There is a wealth of articles and write ups about the cost advantages of offshore outsourcing with a majority claiming anywhere between 40-50% savings.
However, offshore outsourcing has come under attack recently. There is an outcry against outsourcing by parties in the US and UK because of the loss of jobs to people in these countries. Many have pointed out actual costs and poor quality of service as the hidden truths behind the attractive packaging.