Should We Abolish Private (fee paying) schools?

At the recently held conference of the UK Labour Party, delegates voted to abolish private (I.E. fee-paying schools), https://www.theguardian.com/education/2019/sep/22/labour-delegates-vote-in-favour-of-abolishing-private-schools.

The above decision strikes me as iliberal and an attack on the freedom of the individual to spend their own money as they see fit.

The philosophical underpinning of the decision is the belief in equality. Why (proponents of a ban on private schools argue) should a t...