It's fair enough to disagree with private education on a fundamental societal basis. But the thing is, that's idealism. We have to face reality - these schools exist, there are kids in them. In most cases, nothing fantastical is going on inside. The class sizes are a bit more controlled and there's more extracurricular stuff and the power to expel is present and used, which helps a bit with discipline and behaviour. If you have a good state school that your kids use, then great. But plenty do not. I found myself in an unexpected situation with an SEN child, for example. That's how mine ended up in private (thankfully now adult so no VAT for me to pay).
I do therefore think that the word spiteful is appropriate. Kids are in these schools. This policy is fucking some families/kids very hard - the reason for the word spiteful is that the policy isn't going to make a blind bit of difference to state schools. It's hurting private schools as a fuck you to the rich. Which is indeed spiteful.
Jealousy? I'd say there's a lot of jealousy in education. I, for one, am extremely jealous of people living in lovely properties which give them access to lovely state schools. Because I resent having to have paid for my kids' education when some people in different areas got the same quality education for absolutely nothing.