The vast majority of spending in any educational institution is on staff salaries. The majority of private schools are not Eton with huge estates and vast reserves - their budgets are just like any school’s budgets, with staff salaries the highest spend. Absorbing the cost of the VAT would probably mean getting rid of staff - other people’s jobs. Is that OK? Absorb the cost of the VAT by making a few staff redundant? That doesn’t sound to me like a net gain for the U.K. economy/tax take.
If I phrased what you’re arguing as “private schools to make 20% of their staff redundant in order to pay their equivalent of their salaries to the government in tax”, does that sound quite so appealing? It kind of spoils the “sticking it to the poshos” narrative, doesn’t it, because it makes it clear that the costs are in ordinary people’s jobs (private school teachers don’t earn big money, they are ordinary people); and especially in the NI and tax they pay, and their contribution to the economy, and so on.
Most private schools won’t actually want to make their staff redundant - especially with no warning in the middle of the year. So they won’t be able to just absorb all the VAT rise.
This whole policy is an economically illiterate one which only appeals to people who don’t or can’t really think through the consequences on a broader scale - they just like it because they think it’s an opportunity to punish rich people’s kids — plenty of examples on this thread — and recycle the misleading narratives about “tax breaks” that are misinformation about the issue. If Labour announced that they were slapping a tax on any other area of the economy that wouldn’t be permitted under EU tax law, and would force job losses, closures of businesses and negatively counterproductive effects on other areas of the economy, people would be up in arms asking why they were doing it. On this issue, though, they’ve got loads of people cheering on a back of the envelope policy they don’t understand just for spite.
And I say this as someone who’s previously voted Labour all my life and who also works in public education. I won’t be voting Labour again because this is a poorly constructed, counterproductive, anti-education policy that is designed to delight the stupid but which will be a massive own goal in the end.
It’s also a policy that they can only have because of Brexit (another massively ignorant policy that delighted the stupid but has cost us massive economic harm). It’s utter mendacity to be enacting any policy that would need to be reversed instantly if we were to rejoin the EU and then lie to the public that it’s about taking away “tax breaks”.