I'm private school educated, work in state and my children are in state.
The reason there seems to be so much 'angst' (such a snidey word to use about parents who are worried about their children's education) is as follows (pull up a chair, short lecture to follow)...
I don't know about other areas but where I am the grammar schools take all the most academic children and the rest are in the other schools who then take those children on to fulfil their academic potential in varying degrees of success. The grammars (as much as any school can) seem to be able to provide 'guaranteed' academic success (so they should, they have the brightest children). So parents boil it down to Grammar =academic success, non-grammar = academic lottery. You don't have to point out the flaws in this argument to me but there you go, that's how it is. And so we all fuss and worry and tutor and disapprove and grumble about the system but we play the game because we are parents who want the best for our children and in the areas where there are grammar schools exist the best (defined purely by academic results) is grammar.
I'm sure this is all perfectly obvious but for those lucky buggers not in grammar school areas with good state school accessible, do count yourselves lucky. I see no reason though for anyone to be belittling the concerns of those who don't have it so straightforward - whether it be grammar or crap schools in their catchment area or private schools. There are those who have no 'good' schools within their catchment whose children will thrive and succeed and those whose children go to grammar and crumble under the pressure.
I have no interest at all in independent schools admissions, it's not for me but I understand completely why they are just another group of anxious parents, trying to pick the right school for their child. A lot of private schools are tough to get into so there's still a scramble for places as there is with state schools.
As a very wise woman said to me once: the only way to choose the right school for your child is with hindsight.
So endeth the sermon. Go in peace and educate your child into being a decent, kind and honest person, it's the best a lot of us can do.