The Vanishing Cabinet had not been fully mended.
In the books, Fred and George shoved Montague into the Cabinet in Order of the phoenix. According to his account after he Apparated out, he was stuck in some sort of limbo. He couldn't fully be transported from Hogwarts to Borgin and Burke's, nor could he come back to Hogwarts fully. But he could hear snatches of conversation from both sides. This was what gave Malfoy the idea to use the Cabinet to bring the Death Eaters into Hogwarts.
We know from a scene in the movies that the Cabinet was broken (since the movies didn't mention the Montague incident). Malfoy put an apple into the Cabinet, which transported the apple to Borgin and Burke's, and back. When the apple came back, however, there was a sizable chunk cut out of it. And since then, Malfoy has presumably been trying his best to fix the Cabinet.
The next scene shows Malfoy placing a bird into the Cabinet. This is after he had been trying to fix it for some time, and wanted to test it out. And it seemed to work in one direction. The bird was transported safely to Borgin and Burke's, which is why it was still singing.
However, the Cabinet wasn't fully fixed yet. So when the bird was transported back, most likely, another sizable chunk was cut out of it (that wasn't explicitly shown) and it died. This meant that it would be safe for someone to transport from Hogwarts out to Borgin and Burke's, but not safe for someone to come in. This meant Malfoy still had some work to do.
The scene was meant to show that while Malfoy hadn't completed his job yet, he still had made some progress, where the trip from Hogwarts to B&B was safe after he partially mended the Cabinet. But the trip back to Hogwarts wasn't safe yet.