So why did Prince Nikolai go to Herlufsholm and why is this school not selected for Prince Felix? I am just curious and wonder whether school fees are perhaps an issue?
Why Nikolai preferred to go to Herlufsholm, rather than signing up for a high school in Copenhagen is of course something that is open for speculation.
Boarding schools are subsidized but it's still pretty expensive to send your child to one, especially one of the better boarding school and Herlufsholm is one of the best boarding schools in DK. - As such they tend to attract children of parents who have the means (and as such also the status) to send their children there.
The pupils of Herlufsholm also tend to form a lifelong network, which comes in very handy in the future, not least in a small country like DK.
Herlufsholm was the second choice for Felix, according to himself.
What happens is that people sign up for which high schools they wish to attend. In Felix case it was Gammel Hellerup High School, close to where he lives (and still in a very affluent neighborhood mind you). With Herlufsholm as the second choice and presumably another (state) high school as the third choice.
Okay, if there is not a vacant place at Gammel Hellerup High School, then it will be checked whether Herlufsholm has a vacant place (if they want him and if his parents can afford to pay the fee that is.) and if they decline then it's the third option. And if there is no room at the third high school the authorities will allocate a place for him at a fourth high school.
Gammel Hellerup High School is run by the state, so it's free of charge.
What happened was IMO that Felix and most of the boys in his class, whom he seems to be good friends with, all decided to apply for Gammel Hellerup High School and as such stay more or less together for three more years.
All state/public schools in DK, up to and including high school level (and that includes most trade and technical schools as well) are free of charge.
Quite a lot of children attend private schools though. (Our oldest went to a private school, while our youngest attended the local state school.) But the fees are heavily subsidized, so it's generally not that big a burden on the family economy.
But Archduchess Zelia certainly has a point when she says that the school M&F's children attend is a "private" public school. Apart from having a level that ranks among the best state schools in DK, it is located in an affluent neighborhood and as such have a majority of pupils who live in that area - of affluent, influential, well educated and highly committed parents. That rubs off on the school of course. That also applies to the high school Felix is going to attend.
There are of course pupils of less fortunate parents in these schools, but they are very much in the minority. And the school is not that sought after by less affluent parents. It's simply a question of: Will your child fit in and be comfortable there?
In the case of Gammel Hellerup High School, many who are to sign up for a high school may deselect this high school, if they come from a more modest (in this context normal) background and have to rely on SU and part time jobs for their pocket money. SU is the amount all pupils in trade schools and high schools get from the state. It's not a loan, it's money in the pocket while they study to be used at their own discretion.
SU is not that big an amount, but certainly better than nothing(!). So the question is: Will you sign up for a high school, where a number of your fellow students spend an amount that is equivalent to the monthly SU in a day(!) and who live a lifestyle you simply cannot keep up with - and who (in some cases) may be terrible snobs as well?
Or will you sign up for a more "normal" high school, where your fellow students are more like yourself? Perhaps also politically.
Especially as the education can be just as good or even better at an "ordinary" high school.
Hence "private" public school.