> This whole system only builds one type of object. He thinks that his solution is better because it’s more extensible.
> I can’t make him see why it’s bad.
Schools teach OOP as though adding new types of objects is the norm—like every type of software construct is actually a GUI widget in disguise and we're going to be adding new interoperable subclasses every other week, so we may as well get the infrastructure set up to make that easy.
In most real world applications, the only type of object that behaves that way is, well, GUI widgets. Nearly every other type of construct in a typical system will have at most one implementation at a time (possibly two during a gradual transition). Factories, builders, and the whole design pattern menagerie aren't particularly useful when for the bulk of a system's life they're all just proxies to a single constructor.
I don't know if there's a good way to teach this out of someone besides just letting them experience it, but that's the insight that he needs—different types of code have different maintenance characteristics, and the tools he's been given were developed for a very specific type of code and don't apply here.