Since the ‘50s, there have been voices that governments should cease to operate schools and limit themselves to financing it via a voucher system and controlling schools’ compliance to quality standards.  In the early ‘80s, this has been implemented in Chile.  There are three types of schools: private ones freely charge fees, private subsidized that have a limited fee and public.  The quality and equality of the school system fall short of expectations.   This paper proposes a qualitative model to explain what is going on.  Families are assumed to prefer higher performing schools, teachers prefer better labor conditions and schools prefer favored pupils and better teachers.  Richer schools attract more favored families that enable improved results due to the favored-pupil effect; additionally their ability to charge higher fees allows them to attract the best teachers, which further enhances their advantage.  We find 5 positive feedback loops.  The result is a process of concentration of favored pupils and good teachers that increases inequality. It is concluded that there are unequal conditions amongst the types of schools, and as long as they persist, no initiative in favor of more equality will succeed