Apparently, in the United Kingdom, grammar schools, which select 11-year olds based on test results, are controversial, as there is a debate as to whether they do or don't enhance social mobility, opponents arguing that in practice, grammar schools are not accessible by lower/working class children. On the other hand, public schools do not appear to be subject to a debate, despite very high fees (Eton charges £33k/year) and a strong association with ruling classes.
Is my impression that there is more debate surrounding grammar schools than public schools. Is my impression correct? It would appear to me that the arguments against grammar schools, are more clearly applicable in the case of public schools. Then why is it that groups opposed to grammar schools not point their arrows at public schools instead or as well?