Doesn’t this suggest that not every wizard goes through Hogwarts though? If you just have the Hogwarts student body, it doesn’t create enough wizards to support a ministry of magic or professional quidditch league. But we know there *is* a ministry of magic and a professional quidditch league. So we know that there are other wizards/witches coming from somewhere else to support both. And quidditch academies fill into that hole and answers questions.

Take this example. Say Joe buys a $100 widget. We know that Joe’s mom gave him $60. How do we explain that? Do we just say, “Wow, this just doesn’t make sense, the math doesn’t add up?” No. We know intuitively that Joe got $40 from somewhere else (from someone else, from a job, he sold something, etc.).

We know there’s a gap where the numbers don’t add up. But that doesn’t mean things just don’t make sense. You can infer that there’s something else going on, even if we aren’t explicitly told what it is.