All these threads ever prove, time and time again, is that nobody likes paying more tax. Which is not surprising. What they also explain is how unbelievably difficult it is to try and increase tax paid by the wealthiest in society.
People will always come up with reasons why it is inappropriate for their specific scenario, a proportion of which will of course be very valid.
90% of private school parents have an income in the top 10% of earnings in the UK. 85% are in the top 5%. This is simply an extra tax on those high earners who are choosing, for whatever reason, to use independent schools.
All the rest is just smoke and mirrors.