Since the rise of the labour movement, sending your kids to private schools has been largely seen as either a moral failing like in Switzerland, or an admission that your kid is so dumb that you need to buy them a diploma from somewhere else. For a very long time there were hardly any in Norway at all.

To take your example one step further: This same argument is part of the reason why in Norway there are heavy restrictions on private healthcare providers offering necessary services to the public - the public healthcare system has a near monopoly on this. Private providers can provide elective surgeries etc. like breast implants and other cosmetic surgery that is not (usually) covered by the public healthcare, but are mostly prevented from offering services covered by the public healthcare system.

Here the argument goes further: It will ensure everyone has an incentive to ensure the public healthcare is good enough. But it also will ensure that private actors are not substantially draining the public system of resources, such as e.g. doctors that are substantially subsidized by the public education system in the first place.

Basically going private is seen as immoral queue-jumping that will indirectly deprive more needing patients of treatment by reducing the available resources.

> known as "public" in Britain, to confuse us all

It's worse. Not all private schools are public schools. It is first and foremost used about some of the oldest, most exclusive private schools, but "public" here comes from being open to the (paying) public irrespective of e.g. religion or occupation or where you live contrary to e.g. private schools run by religious groups and similar.