I wouldn't say that I am particularly obsessed with being upwardly mobile, but like many other MNers am first in the family to have gone to university, get a professional (and co-incidently well-paid) job and become a home-owner (if we ignore the right-to-buy revolution which helped those of my family who were in council housing, but not those who were in private lets such as my parents).
I'm obviously conscious of the extra options that were open to me because of my education, and I would like the dcs to have a similar range of options open to them. But in an meritocracy say, in order to ensure that children in deprived circumstances get the same opportunity it may be necessary for the prospects of my children to diminish. And it must be hard not to instinctively help your child to develop their fullest potential - surely most of us do that to some extent whether it is through our choice of schools, or encouraging our children with their homework, paying for additional coaching or activities etc, or through the attention that we give them ourselves - all of this could be construed as an unfair advantage.
Ultimately it is very difficult to create a level playing field, because some parents will always seek to help their children, and that will alwasy be unfair to those children whose parents aren't interested, or don't understand the nature of competition for different fields.
I can understand why parents who have paid for private schools feel strongly against the positive discrimination implied by some of the university admission discussions. But mainly because it is discriminating against parents who have chosen to support their children in a particular way.
As for Oxbridge, of course these are not the "best" universities, but a large proportion of successful business leaders have been there - 22% of the FTSE100 CEOs are Oxbridge graduates (and only 72% of FTSE CEOs are British). The only other unviersity to field so many has been Harvard. And I wouldn't be surprised if a similar proportion of Magic Circle and Big 4 partners had a similar background. Certainly Oxbridge doesn't have the best degree courses in every subject (I'd possibly say in many subjects!), but to say that it is no indication of their ability seems a bit strong. But then an Oxbridge education may not be solely about the degree course.
That said I have to say that I have never had to justify my choice of university whereas I often hear people explaining why they didn't apply to Oxford or Cambridge. Actually that's not quite true - but I've only had to justify why I didn't choose one other university (and it wasn't Durham or Bath).