Category not loading template
The template path specified in the admin should point to a single file, not a directory.

index files are only loaded when the Craft router falls all the way through element URIs and starts to look in your templates folder—in your case, that would be local.domain.com/pupil-of-the-month.

I suspect the confusion lies in that the router does eagerly look inside a directory for index.* templates in some narrow cases (as stated above), but that the pattern is not adopted by Category/Section/Tag settings.

See the official Routing Docs for more information about the process Craft uses to resolve the template for a request.