Ok. I may have over-egged it by using the word "everything" and I should have said the vast majority.Starmer pssisses me off no end - but that is simply untrue
None of them, ever, would put VAT on private schools
And, as has been said - there is no manifesto yet
On that though. He knows that the vast majority of the country are against private schools. Only 7% of kids are privately educated and charging VAT instead of doing something about getting rid of them altogether doesn't actually change anything about the imbalance between the rich that can attend them and the rest that can't. Even the majority of the centre-right Tory voters he is seeking to attract aren't wealthy enough to make use of private education. Proper Tories probably see it as a benefit because the people that can barely afford to go there shouldn't be mixing with them anyway.
A sensible Tory would realise that a policy like that could be a vote winner but they wouldn't do something that would go against their base if they don't have to. Labour regularly do things that go against their base to try and win votes.