The principal point of private/public school education is to get the best out of the child, whatever the child's abilities, character, or difficulties in learning.It's an exercise in making the most of the material. That's all. Parents think that state schools can't do that. The private school should have smaller classes, more personal teaching, better 'pastoral care', better facilities, better funding and so on.If the boy or girl can't do maths after that, it's a certainty, or so the belief is, that they'd be no better with state education and the chances are they'd be even worse.
You can add in 'the old boys' network' and supposed cachet of some public schools, too.