The human brain stores information. I would not call it a database.

Let's start with your statement: "If it can store and retrieve data, it's a database." One of the notable characteristics of human memory is that it is not reliable. It does NOT reliably retrieve the data that it stored -- and I don't just mean that we forget some things, I mean that many of our memories are factually incorrect.

Human memory is extraordinarily USEFUL, but in order for the term "database" to have a useful meaning, I have to categorize human memory as a form of information storage that is NOT a "database".

This would mean that a floppy disc (hardware) and the filesystem used to arrange the bits thereon (software) are each a database. How is breaking down the distinction between database, filesystem, and storage medium helpful?