The arguments 'life is not fair' and 'it's natural for some people to do better than others' are stupid. Thankfully the vast majority of people don't buy into either of those fatuous ideas anymore or women and the working classes would still not be voting let alone being educated even at primary level and certainly not in HE. There is nothing 'natural' about some people getting into Oxbridge and some people not and it's all very well to accept the status quo dismissing any arguments for change as 'life is unfair' if you're one of the privileged.
And it's equally crass to suggest that asking for more equality in education is somehow akin to establishing a communist state like the ones that have failed. There are many other countries which have a more equal education system and strangely enough more social ability without being communist. In fact, pretty much every country in Europe, the US and Scandinavia does. Britain is the worst in these respects.
The problem with systems where you have an elite (and this applies also but on a sliding scale to private schools, grammar schools and faith schools) is that everything else is going to be second best. The elite institutions will attract more funding, more applicants, more teaching exerptise, a better reputation and then more funding, more applicants ... and yet they serve a tiny and privilege minority of society as a whole while those serving the majority who probably need more funding, more expertise etc etc don't get it.
Now private schools are one thing but it's something else when we all pay our taxes for institutions (grammar schools, faith schools and top universities) that only a few (usually the wealthy, the well-educated and the pushy) can access.
I can see why you might want universities to specialise in particular fields (medicine, languages, whatever) but I can't see why we need to have universities organised into a hierarchy.
Likewise with schools. Why can't children just go to their local school which should be just as good as the local school 5 miles away and 100 miles away. People can't be prevented from opting out and paying but it shouldn't be taxpayers who fund the education of the privileged few.