How did Dumbledore not know that the Vanishing Cabinet was one of a pair?

Question

In Harry Potter and the Halfblood Prince, Draco Malfoy uses a Vanishing Cabinet stored in the Room of Requirement to bring in a bunch of Death Eaters to wreak havoc and kill Dumbledore. Before (not) going in for the kill, the two have a bit of a face-off where Draco explains the ins and outs:

‘So tell me, while we wait for your friends… how did you smuggle them in here? It seems to have taken you a long time to work out how to do it.’ […]
    ‘I had to mend that broken Vanishing Cabinet that no one’s used for years. The one Montague got lost in last year.’
    ‘Aaaah.’
    Dumbledore’s sigh was half a groan. He closed his eyes for a moment.
    ‘That was clever … there is a pair, I take it?’ […]
    ‘The other’s in Borgin and Burkes,’ said Malfoy, ‘and they make a kind of passage between them. […] I was the only one who realised what it meant – even Borgin didn’t know – I was the one who realised there could be a way into Hogwarts through the Cabinets if I fixed the broken one.’
    ‘Very good,’ murmured Dumbledore. ‘So the Death Eaters were able to pass from Borgin and Burkes into the school to help you… a clever plan, a very clever plan… and, as you say, right under my nose…”
_{Harry Potter and the Halfblood Prince, ch. 27 ‘The Lightning-Struck Tower’}

Going by this, Dumbledore clearly didn’t know that the Vanishing Cabinet was part of a pair. I’ve just realised that there’s a bit of a snag with this, though.

We know from Order of the Phoenix that the Vanishing Cabinet in question was not always stored in the Room of Requirement. The first time we hear about it, when Fred and George push Montague into it, it is located somewhere where students roam freely:

‘Malfoy just docked us all about fifty points,’ said Harry furiously, as they watched several more stones fly upwards from the Gryffindor hour-glass.
    ‘Yeah, Montague tried to do us during break,’ said George.
    ‘What do you mean, “tried”?’ said Ron quickly.
    ‘He never managed to get all the words out,’ said Fred, ‘due to the fact that we forced him head-first into that Vanishing Cabinet on the first floor.’

Wherever exactly the Vanishing Cabinet was at that time, it was on the first floor, in a location where members of the Inquisitorial Squad and students (well, Weasley twins at least) both found their way during breaks between classes during the day. So presumably in a corridor or hallway somewhere, or perhaps a seldom-used classroom.

Now Draco does say above that it was broken and “no one’s used [it] for years”—but presumably it must have been functional at some point earlier on. As TGnat points out in the comments below, Nearly Headless Nick convinced Peeves to knock over and severely damage a Vanishing Cabinet on the first floor (or rather: right above Filch’s office, which is listed on the Wiki—without sources—as being on the ground floor) in Chamber of Secrets (ch. 8 ‘The Deathday Party’). If this is indeed the same one, it was functional only about four and a half years previously.

Leaving aside the question of why Dumbledore would leave a non-functional (and possibly dangerous) Vanishing Cabinet standing in a public place like that, I can’t imagine how he could not know what it actually was.

The only likely way for that to come about would be if it had been broken all the time Dumbledore had known it be there; that is, at least since before his time as a teacher (so at the very least about 60 years) and perhaps even as a student (so at least 90 years). This seems unlikely. Who leaves a broken Vanishing Cabinet in a public corridor for 90 years? (It certainly couldn’t be the one from Chamber of Secrets in that case.)

But if the Cabinet had been in working condition while Dumbledore was there as a teacher or headmaster, surely someone would have used it at some point and realised the passage it forms with the one in Borgin and Burkes, and Dumbledore would not have been so surprised to hear of this passage in the tower.

So how did Dumbledore have the Vanishing Cabinet standing around the school for so long without ever knowing that it was one of a pair and led to Borgin and Burkes?

Answer 1

Because, as Dumbledore himself acknowledges, the plan was very very clever.

It would appear that vanishing cabinets normally come in singles, simply allowing the user to vanish an object (or indeed themselves) until a later date, much like a conjurer's box

MR. WEASLEY: They were all the rage when Voldemort first rose to power. You can imagine the appeal. Should the Death Eaters come calling, one needed only slip inside and disappear for an hour or two. But they’re tricky contraptions. Require a tremendous amount of looking after. Eventually they fell out of favor. - _{^{Harry Potter and the Half Blood Prince (Film)}}

The fact that two of them were linked and that Draco was able to use this linkage to bypass multiple layers of protection around Hogwarts was apparently a surprisingly cunning and deeply unexpected move.

Then, as though he could not help himself, he said, ‘I had to mend that broken Vanishing Cabinet that no one’s used for years. The one Montague got lost in last year.’
‘Aaaah.’
Dumbledore’s sigh was half a groan. He closed his eyes for a moment.
‘That was clever … there is a pair, I take it?’

For the record, a broken vanishing cabinet isn't completely useless since you can use it as a cabinet. This would explain its continued presence at Hogwarts.

Answer 2

A number of points.

Dumbledore didn't know everything about Hogwarts.

Consider this conversation he has with the Headmaster of Durmstrang.

"Well, Dumbledore," said Karkaroff, displaying his yellowing teeth to their fullest extent, "we are all protective of our private domains, are we not? Do we not jealously guard the halls of learning that have been entrusted to us? Are we not right to be proud that we alone know our school's secrets, and are right to protect them?"

"Oh, I would never dream of assuming I know all Hogwarts' secrets, Igor," said Dumbledore amicably. "Only this morning, for instance, I took a wrong turn on the way to the bathroom and found myself in a beautifully proportioned room that I have never seen before, containing a really rather magnificent collection of chamberpots. When I went back to investigate more closely, I discovered that the room had vanished. But I must keep an eye out for it. Possibly it is only accessible at five thirty in the morning. Or it may only appear at the quarter moon - or when the seeker has an exceptionally full bladder."

(Goblet of Fire, Chapter 23, The Yule Ball)

The fact that Dumbledore didn't know about the Room of Requirement is a big piece of information, especially considering its importance in the later books. Not only is it the location of Harry's DA meetings but it's where Voldemort hides one of his Horcruxes and the key to his plans (through Draco) to assassinate Dumbledore. Yet when Dumbledore stumbled into it he mistook it for a temporary toilet and never came close to guessing the room's true significance. As Harry notes in the final book, this may have been because Albus Dumbledore was a model student and never had need of a room to hide anything from the teachers. Harry, however, got into plenty of tough scrapes. Dumbledore may have been at Hogwarts for years but even a lifetime at Hogwarts isn't enough to plunge all its secrets. Dumbledore never found out where the Chamber of Secrets was, for example.

The Vanishing Cabinet was one of many ornamental pieces.

Hogwarts is fricking massive.

There were a hundred and forty-two staircases at Hogwarts: wide, sweeping ones; narrow, rickety ones; some that led somewhere different on a Friday; some with a vanishing step halfway up that you had to remember to jump. Then there were doors that wouldn't open unless you asked politely, or tickled them in exactly the right place, and doors that weren't really doors at all, but solid walls just pretending. It was also very hard to remember where anything was, because it all moved around a lot. The people in the portraits kept going to visit each other and Harry was sure the coats of armour could walk.

(Philosopher's Stone, Chapter 8, The Potions Master)

Hogwarts is a logistical nightmare. If Dumbledore wanted to make it entirely child-friendly then he probably would have started with the violent trees and three-headed dogs. However, I doubt that he was even particularly aware of the Cabinet's existence. He would've walked past it plenty of times. The Cabinet was merely one of hundreds of ornamental objects littered around the corridors (alongside paintings, suits of armour etc.) and most people presumably weren't aware that it was a Vanishing Cabinet at all. Malfoy only realised what the Cabinet could do when he heard Montague's testimony. As far as Dumbledore and everyone else was concerned it was just 'that cabinet we sometimes walk past on the first floor'.

The Vanishing Cabinet wasn't dangerous to bystanders.

There isn't too much info on the magic of how the Vanishing Cabinet works. However, we do get two glimpses of the two Cabinets Draco ends up using in Chamber of Secrets as part of some very clever (and early) foreshadowing by Rowling.

Harry looked quickly around and spotted a large black cabinet to his left; he shot inside it and pulled the doors to, leaving a small crack to peer through. Seconds later, a bell clanged, and [Draco] Malfoy stepped into the shop.

(Chamber of Secrets, Chapter 4, At Flourish and Blotts)

Clearly getting into the Vanishing Cabinet isn't enough to activate it - or Harry would've been instantly transported to the first floor corridor at Hogwarts. Maybe you have to completely close the door. Maybe you have to concentrate on the other location or perform a spell. The Cabinet in Hogwarts wasn't really doing any harm either before or after it was broken later that same year.

Nearly Headless Nick came gliding out of a classroom. Behind him, Harry could see the wreckage of a large black and gold cabinet which appeared to have been dropped from a great height.

Chamber of Secrets, Chapter 8, The Deathday Party)

In conclusion, Harry is the only character other than Draco who really comes into contact with the Cabinets in the series. If he couldn't put two and two together then we can scarcely expect Dumbledore to.