I think this articulates the situation rather well, and it is somewhat reassuring to think of it in those terms. At least when people like Leah5678 pop up, it is easier to make sense of their position.
Hypocrisy is a defining feature of left-wing politics, and it never works out for the left when they attempt stunts like this. It hasn't worked out for state schools - the most socially selective state schools are "comprehensive" schools, not grammar schools; and the near abolition of grammar schools has been associated (causally or casually) with a threefold decline in educational mobility.
My children were privately educated from three, went to one of the Clarendon Commission's nine schools with academic scholarships, Oxford (one as a scholar) and then into the higher reaches of traditional (non-medical) professions, where they have garnered accolades.
They could have been educated at the state's expense at a local comprehensive school (then ranked in the top 50 for Oxbridge entry by the Sutton Trust) or at a nearby grammar school (then sending as many children to Oxford and Cambridge as the private school they went to).
Faced with that choice in the current climate, would we do the same again? Absolutely, because at age 18 human beings are largely fully formed. By then if they have been well educated they are usually capable of dealing with setbacks. As far as Oxbridge and future employment is concerned, it won't take employers long to develop alternative metrics.
Given that Oxbridge are systematically rejecting the best (and in the same way that an A grade can never be considered to be equal to an A star) a privately educated job applicant with a first from Bristol, Edinburgh, etc. logically must now be considered, ceteris paribus, a better candidate than a state educated applicant with a second from Oxford or Cambridge.
With universities discriminating according to school type, employers will in time also learn to - and in the right way.