Someone has probably already covered all my points much better. But what the heck. If you're real OP, you're finally getting some of the data to show why the stats are the way they are. But here's the answer I didn't manage to send before!
I don't have the detailed evidence some of the other posters have linked to though I've seen much of it at some point.
This is long, OP.
Some of the earlier answers haven't really given you a fair hearing, and I'm trying to talk to the person I think you really are, and explain how I see this, and some of the factors behind this statistic.
If I were in your shoes, I might feel everyone was jumping on me although I don't think all of it is intentional. This is long and complex - some of these ideas just are.
If you really want to understand some of these factors please bear with me.
(Others, please don't jump on me - I've probably missed whole areas I haven't got experience of.
And misestimated the importance of different factors.
I'm afraid that's the social bubble effect.
And this is an explanation written mainly for the OP, who appears to be in a different social bubble and maybe hasn't been exposed to some of these ideas before.
If this comes across wrong - please bear in mind it is aimed at one person in particular. ).
I understand where you are coming from, OP, with your idea that the average cohort at private school is more intelligent that the average cohort at state school.
And actually, I think you are probably right for a variety of reasons I'm not discussing here.
But you have some blindspots regarding the students an elite university are probably after, and the correlation between wealth and intelligence in society.
There are a lot of careers which don't earn $$$$, but which demand extremely high levels of intelligence and focus.
As someone pointed out, university lecturers are at the cutting edge of furthering knowledge, but wouldn't be able/necessarily want to privately educate a child.
In fact, the really bright kids probably actively don't pick high paying careers.
(From my highly selective school, it was lower set pupils who went on to become lawyers and doctors - ie degrees which would fund private schooling.
The higher set students mainly took Natural Science, Maths and Engineering degrees, none of which pay particularly highly unless you make a sideways step into banking, etc.
So the very brightest pupils are disproportionately likely to state educate their children compared to the slightly less bright pupils.
Their criterion is typically more like "the most demanding work I can find, pays OK" not ""good pay, fairly interesting").
Then there are the children of parents all over the social continuum who would never consider a private school because that's not what they had.
Just not in the experience range.
They could earn a lot and not consider it.
And intelligence is all over the demographic spectrum too.
The brightest child I have ever met (at age 8 it was obvious he's heading for Oxbridge/equivalent maths - both the ability and the all-consuming, lasting interest) has a single mother who's a reflexologist and doesn't come across as smart.
In a similar vein, the child from my DC's old (state primary) class that I think is the most likely to get into Oxbridge has a tradesman father and a TA mother.
Their sibling is fairly similar. (3 from that class are bright enough they 'should' be considered by your metric, but only one has a decent chance as they have the organisation level to make it happen)
(BTW, yes, I can judge!).
And one of your respondents highlighted the 5 children in authority care who got into Oxford.
As a result, in some cities, the whole of the top sets of state comprehensive schools are made up of the children of parents educated at elite universities, and their intellectual peers, whatever their background.
There are comprehensive schools with 'self-study GCSE maths' sets - where the second sets are still predicted 8-9.
Your 'nature' fact - honestly, genetics is a bit more random than that: Statistics means only a percentage of children with parents right up the tail of the distribution are going to be as smart as the parents.
And there are a lot more 'average-plus' parents around.
Now let's say a child is likely to have +/- x IQ points compared to the parents based on random genetic factors popping in and out in combination, fetal exposure to medication/chemicals, placental nutrition factors, and a whole bunch of other stuff, what do you think the parents of a really bright child are typically going to be like?
An awful lot of them aren't going to be as bright as the child.
(Maybe the stars didn't line up for the parents but they do for the child)
NB - Please don't jump on my stats/genetics - it's not my specialist area and my point is that the intelligence of the parents does not predetermine the intelligence of a child to as great a degree as you might think.
(Nurture - sure, the private school will make sure fewer children under-perform their academic potential. 2 of the children in that class might get in...)
Then there is the effect of tutoring.
While it is easier now to tutor a child for selective school entry, that also means a bunch of kids at selective schools don't really deserve to be there. They might look bright on paper, they might get good exam grades because of high levels of support, but they really aren't anything special.
(I'd say the Oxbridge students probably weren't tutored but actually my local super selective private recently turned down 2 I think are future Oxbridge candidates.
They weren't tutored.
Maybe some of the selective schools are just picking the wrong kids ... ).
Oxbridge want a particular kind of focus and drive (dare I say, obsession) for the subject.
This is likely to be different from the skill sets / aptitudes which made many fee-paying parents their money.
"I want to earn well and have good status" and "I HAVE to do a job which fundamentally improves the knowledge of society and creates the technologies and science of tomorrow and where I am continually challenged" are very different attitudes.
Oxbridge probably want the latter.
Up to a point, intelligence will help you make more money and do a more complex job well.
But the people Oxbridge want may well not be in the private school system because their parents aren't wealthy, haven't considered it, or aren't interested in money and have self-selected their children out of it by career choice.
The fact that there are a vast number of "average-plus" intelligent children in the private school network does not mean there is a huge over-representation of Oxbridge-bright students there
(I'm not arguing there are not 'some' more, btw. ).
It's a very appealing idea that wealthy people are wealthy because they are intelligent.
(And, even therefore that poor people are mainly poor because they are stupid or lazy).
It's easy to believe, especially if what you are exposed to reinforces your views and if you see intelligent people around you working hard and earning well on a daily basis.
Many newspapers also reinforce this viewpoint.
I believed it when I was younger because it's what I was told.
And it 'makes sense' seen from that point of view.
The evidence actually shows that if a privately educated and a deprived child with the same grades get onto the same course, the deprived child outperforms the spoonfed child.
They are just a higher quality student in the first place - to get the grades they probably had to be hugely self-motivated and teach themselves an enormous amount if the teaching was sub-par.
The workload in the private system means an average student has learnt a lot more about what hard work is than an average state student. They'll get higher grades, they'll be more confident. This doesn't actually make them the student Oxbridge/similar want.
I'm actually not sure that universities are biasing against private students - but by bringing in entrance tests which test for the traits they want (subject relevant intelligence), it's now less likely for a highly supported child who is not so bright to get in.
If anything, the fact that state school students are less well supported and typically less confident suggests that private school students still have an advantage.
The confidence to bludgeon your way through an interview, finding more ways to approach a problem will stand a candidate in good stead, whereas a less confident student is more likely to fall at this hurdle and not show their real ability.
The exams now allow more of an objective look at the real ability of a student under standardised conditions and allow less confident but very bright students to shine.
(Actually the more confident students are probably less likely to be impaired by exam nerves again, but it's a start)
(Yes, the exams are tutorable, just like an 11+, but you do need to be at a certain level to even see what the questions are really asking).
Don't feel deflated, though - your privately educated children have more life experiences to draw on, higher confidence levels, a better social network for later in life, etc
They are probably less stressed - they haven't had to make their grades happen themselves, they have just had to do the homework they were set.
They probably still have an advantage in university interviews and honestly in their careers too.
Confidence takes people a long way.
It's just that the students that Oxbridge were after probably weren't present in private schools in the numbers you believed, because so many of them are in the state sector for all of the reasons I've mentioned and more that I'm not aware of or slipped my mind.
And this was always the case, it's just taken the colleges a while to figure it out.
And for that time, private school interview advantage and grade advantage meant that everyone assumed private school pupils must be the brightest.
And now the evidence is finally there to show that poorer students with weaker grades can perform better in their degrees.
I hope that highlights some of the factors which don't jump out at you as much as the idea "we're all bright, so we must have a hugely disproportionate number of Oxbridge students in our midst".
It's the most obvious idea, I agree, and a lot of people believe it but that doesn't mean it is necessarily right.
(Others, yes, I've missed stuff and simplified in areas.
This is long enough!)