I ordered some dogs from a human caravan, and when they arrived the following year, my dwarves dutifully moved their cages to an animal stockpile. (There's a complication to this, which I'll explain below.)
I installed one of the cages nearby, then unselected the dog from it to free it.
A dwarf came by, removed the dog from its cage, and then... instantly put it into a different cage. (The dogs came in wooden cages, and the dwarf moved it to a green glass cage that I had made.) I tried three or four times to free the dog, and each time, the dwarf moved it directly into another cage.
Has there been some change in the cage interface that I'm not aware of? I've never had this problem with purchased dogs before.
A weird event that might be related: Goblins besieged me just as a human caravan was pulling up to my trading post. They killed about 80% of the humans and almost all of the horses. Oddly, the merchant baroness was already in my office making plans for the following year as her entourage was being smeared into red paste.
When I tried to trade with the surviving humans, I got the message "There are no merchants trading right now." So I never got a chance to trade, and I couldn't just steal the items either, since they were flagged as human possessions and unavailable to me. A few years have passed now and this old, inaccessible meat is still lying on the ground. Dwarven and elven traders have come by each year and have traded normally. The humans haven't returned. The baroness is still wandering around my fortress.
Anyway, back to the dogs. I'm wondering why I was able to pick up these dog cages at all, since none of the other human gear is available to me. Perhaps these (admittedly very unusual) circumstances are what brought about the cage-switching bug, if indeed it is a bug.