Why did Dumbledore allow Draco Malfoy to return to school in Harry Potter and the Half Blood Prince?
What prompted Albus Dumbledore to keep the hallowed Hogwarts hallways open to Draco Malfoy, knowing that Draco intended to kill the headmaster?
Because Dumbledore needed Lord Voldemort to think he was getting one over on his former Professor of Transfiguration, so that the Dark Lord wouldn’t have reason to put any other plans in motion, at least not immediately.
…(Severus) Snape said, “The Dark Lord does not expect Draco to succeed… “ “…the boy has had a death sentence pronounced upon him…” said Dumbledore … “Lord Voldemort foresees a moment in the near future when he will not need a spy at Hogwarts?” “He believes the school will soon be in his grasp, yes.” Harry Potter and the Deathly Hallows - J.K. Rowling
As long as Voldemort thought his plan for Draco to kill Dumbledore might actually work, Voldemort would be more likely to sit on his hands and bide his time.
If Voldemort had ever realized Dumbledore knew exactly what he and Draco were up to, Voldemort would have put other plans into play, possibly knocking down Dumbledore’s own already-shaky house of tarot cards.
Sure, Dumbledore was concerned about Draco’s well-being, to a degree, but not really THAT concerned. After all, the health of students wasn’t as important to Dumbledore as destroying Voldemort; otherwise, Albus would have taken steps to remove Draco immediately after the near-fatality of Katie Bell.
The excuse that Dumbledore couldn’t see the connection between Katie’s near-death and Draco needing to kill Dumbledore doesn’t really hold any water; Draco would have been the FIRST dot Dumbledore tried to connect to Katie and there was not even one other plausible explanation, at least nothing that made MORE sense than it being Draco.
So, I don’t know for sure, was just Dumbledore’s verbal line of reasoning to keep a dangerous pawn in play as Dumbledore continued to mislead Voldemort.