Harry Potter is not a person who lives in JK Rowling's head, he's an idea which is shared in various forms by millions of people all over the world.
This, I think, is what people can't get their heads around. It's the idea that there does not have to be a single, correct answer to any question about a fictional character. The idea that something could be deliberately ambiguous, or intentionally left open to multiple interpretations seems to blow people's tiny minds. The idea that an interpretation that was not intended by the author could still be valid seems to make Fandom physically ill.
[And later, in the comments:]
... [this happened because] adults took something intended for "the kids" and got into it themselves. Adults are the biggest kill joys ever who need to know they're right and that the world makes sense etc, and who will annoyingly argue themselves to the ends of the earth in pursuit of acknowledgement.
There's a lot to mine out of an observation like this, so much so that at first I have trouble figuring out how to attack it systematically, like a sandwich that's too thick to bite into properly.
I suspect most of the author's comments about fandom come from being exposed to its noisiest, most reactionary and most hidebound elements — although, sadly, those tend to be the parts of fandom that make the biggest impression, because they're noisy, reactionary, hidebound, etc. It's easy to assume such people speak for the whole of the way fandom works.
What's most interesting to me is the point made about Harry Potter being an idea — a source, rather than a destination — and how fandom deals, or does not deal, with that concept. When we each read the same book, we all walk away from it with slightly different versions of what goes on — and that's by design. We're not clones of each other, and so we bring as much to the book ourselves as the author did when she wrote it.
There's a spectrum of activity here. On the one end, you have the author as absolute tyrant; on the other end, you have the reader as the final arbiter. The real experience of reading something happens smack dab between the two, with some oscillating back and forth.
To that end, I wonder if people like the idea of a single, consistent, correct canon for a given fandom for the same reason they seem to think of fandoms more as environments than finished works. You don't just read something like Harry Potter, if you're really into it — you get into it, as the term has it. You get into it and you sort of set up shop inside it — you try to take over as much of that spectrum of interactivity as you can. In a way, that makes the product even more abstract and malleable: instead of consisting of a specific sequence of events, it becomes more of a free-floating space inside which any number of things can happen.
I'm not singling out Harry Potter as the only fandom that does this; it's a phenomenon that's as old as fandom itself. I'm also not convinced it's a wholly bad thing, because out of such immersivity can come insight and perspective that might not come from just being an outsider. But it's not the healthiest relationship you can have to a piece of material. Among other things, it sounds like it causes that much more energy to be diverted from actually appreciating a piece of work and into trying to own it, to inhabit it.
Appreciation means more than just reading and liking; it also means an understanding of what works and what doesn't, and taking what you can from it and rolling it forward into your own work. I would not be the writer I am today without having read Philip K. Dick, but I know I wouldn't have gotten anywhere if I'd simply tried to emulate his mode, because it's his mode, and it came entirely out of his experiences and point of view. I had to build my own bridges.
The Ferretbrain site, by the way, is at the same time engaging and infuriating — one of those places where I can't say I agree with half of what's posted, but I admire every meticulously-expressed, dry-as-toast, British-humored word used to express it all.