I've made a claim about these circumstances, not about any circumstances.
That's not true. The question here is whether it is fair to confer an advantage upon a child by increasing their chances of getting into their preferred school on the basis that their father attended the same school in the past.
That's a fairly straightforward question, and not one that is difficult to answer.
I already pointed out that this isn't true. The courts have ruled that the discrimination was not illegal. That has no bearing on whether or not the discrimination is just or unjust.
Also I would point out that you don't speak for the vast majority of people in our country, and even if you did, the fact that a vast majority of people believe something does not prove that they are correct. History is full of examples where the vast majority of people believed things (both normative and non-normative) which turned out not to be true.
It's unfair because it discriminates between different groups of children on the basis of facts about their parents.
Suppose that the government decided that they were going to increase dole payments, but only for those people who happened to be born on a Tuesday. Do you think you could provide a compelling argument to show that such a decision would be unfair on those who were not born on a Tuesday?
Don't blame me; I voted for Kodos.
I don't think a child should get a place in a school on the basis of "blood over location" either, but this isn't actually how most admissions policies work. I can't speak for the school in question, as I haven't seen their admission policy, but generally they go something like this: All children are welcome in our school. If we are over-subscribed, preference for places will be given IN THE FOLLOWING ORDER...
Usually, children with an older sibling in the school will be given first preference. This makes sense, I think. Then it is children within a given radius of the school (in the school I work in, this is even clarified as meaning "as drawn in a stright line on an ordnance survey map).
And so on.
To get to the point where you are discriminating on the grounds of where your parents went to school, you are actually quite far down the list and you have already accommodated those who leave nearest to the school.