Non-religious circumcision began in the late-19th century as a misinformed attempt to "cure" boys of various diseases thought to be caused by the prepuce (foreskin).  Doctors in British-influenced nations (including the US) were heavily influenced by the quasi-moralistic views of the Victorian era, and believed that masturbation was harmful.  The practice of surgical genital alteration was also inflicted on females, but to a lesser extent (this practice eventually faded away).  In the early-20th century, the views of the medical establishment regarding masturbation were largely rejected.  However, other rationalizations to modify the healthy genitalia of males were soon invented.  Circumcision is a cure in search of a disease.  Thankfully, all the national medical organizations in the US have finally acknowledged that circumcision is not medically necessary.       

For more information, see the Circumcision Information and Resource Page:

www.cirp.org/library/history