This makes a lot of sense, and is borne out by the positive portrayal of tutoring relationships between Caspian and Dr. Cornelius and Peter and Professor Kirke.

I haven't read Lewis's memoir or letters, but I get the sense from the Narnia books that he values a kind of pastoral freedom and spontaneity that is stifled by the regimentation of the school day. It seems important to him that children have the freedom to drop everything and climb a tree at any moment. :)

There are also a lot of very cruel schoolchildren in the books, and I suspect he thinks the school environment encourages them to be that way. Eustace might be a good example of this, since he begins to change after having a powerful experience outside the school environment.