That's not totally true. When I worked for the Railroad FICA was not taken from your check because they have Railroad Retirement which replaces Social Security. I'm sure there are many others that do the same thing, like Congressional members.
though tey're being phased out, some people don't pay FICA:
There are a number of groups of workers who are exempted from having to pay Social Security taxes:
Federal employees hired before 1984 who elected to continue to participate in the federal retirement program instead of receiving part of their retirement under Social Security coverage.
State or local government workers (police officers, firefighters, and teachers) hired before March 31, 1986 and participating in their employers' alternative retirement system.
Ministers may choose whether or not they will participate in the Social Security program.
Self-employed workers with annual net earnings below $400.
Election workers earning $1,000 or less a year.
Household workers earning less than $1,500 per year.
Minor children with earnings from household work but for whom household work is not their principal occupation.
College students working under Federal Work Study programs, graduate students receiving stipends while working as teaching assistants, research assistants, or on fellowships, and most postdoctoral researchers.
Individuals who are members of certain religious groups such as the Amish and Mennonites.