Parchment
I think the use of parchment is a an example of Wizarding culture being deliberately antiquarian. There may also be an element of economic control at play - parchment is significantly more expensive, and so keeping written works expensive may be a way to keep the lower classes in line. The extensive use of parchment even stupid little notes and homework assignments will help keep poor families away from magical knowledge. If you cannot afford parchment, your children cannot do as well at Hogwarts, and thus cannot do as well in later life.
Paper
Paper is really old, being present perhaps as far back as 300 B.C. in China.1 However, it took a while for paper to reach Europe, sometime around the 11th Century.2 Paper was originally viewed with disdain, unworthy for formal communication, or important works3; something that would definitely influence the magically community. However, it seems that by the 16th Century or so, paper had largely replaced parchment, driven largely by the printing press.4 The Wizarding world does seem to have a sufficient trade in books to stock at least two book stores (one in Hogsmeade and one in Diagon Alley), and I am quite confident that the books give us a view of the press that the Quibbler is printed on. This means that they do use paper books, and paper periodicals.
Any number of fan fiction works I’ve read have speculated that there might be a magical reason for using parchment instead of paper. Most of these have not really made much sense given the above. However one I came across recently does.
Paper doesn’t take magic terribly well: parchment is a single piece of animal skin, a unitary object. Paper is laid fibre from multiple trees, a composite object and as such tricky to get predictable results out of when you enchant it. The more you know, et cetera.5
The reference is to some of the fragmentary descriptions we have from McGonagall’s lectures on transfiguration. You have to be able to visualise the object that you are working your magic on. In this light it is actually easier to see why it might be troublesome to enchant paper. It would be all too easy to have a charm take hold on only a subset of the fibres involved, and thus behave erratically across the document. This makes a strong argument for using parchment (or vellum) for documents that are actually magical in nature (like contracts, tests charmed against cheating, official government or banking forms, etc), but not for standard every day things (like homework, class notes, and letters (unless you are including privacy charms)).
[Harry]: </Harrypedia/people/Potter/Harry James/>/ [Wikipedia]: https://en.wikipedia.org/
©Paper Sizes. “The History Of Paper” International Paper Sizes and Formats Last viewed 2020-08-16.↩︎
©Paper Sizes. “The History Of Paper” International Paper Sizes and Formats Last viewed 2020-08-16.↩︎
Reginmund. “The Rise and Fall of Parchment” All Empires Online History Community 2007-01-10. Last Viewed 2020-08-16.↩︎
Reginmund. “The Rise and Fall of Parchment” All Empires Online History Community 2007-01-10. Last Viewed 2020-08-16.↩︎
AndrewWolfe. The Ghost of Privet Drive Archive of Our Own Last Updated 202008-14. Last Viewed 2020-08-19.↩︎