I know that one of reasons is that Malfoy would be killed by voldemort but if they helped dumbledore to survive they could help Malfoy as well.Voldemort couldn't kill harry because he was hiding so they could hide Malfoy as well.And severus didnt need to be in voldemort's favor.They could just all survive.
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I'm not an expert on ths as many are, but I recall that the curse of the ring was already killing Dumbledore. I thought that Dumbledore asked Snape to kill him.
As Aslan said, Dumbledore had already put the horcrux ring on, out of a desire to see his family--he had guessed that the horcrux was in fact the resurrection stone; that is, one of the deathly hallows. Meanwhile, Dumbledore had asked Snape to spy on Voldemort for him by pretending to become a death eater and spying for Voldemort. This was quite feasable since Snape was a teacher at Hogwarts and so could easily "spy" on Dumbledore. Therefore, and we see this in the scene where Snape was trying to keep the ring's curse from spreading, Dumbledore asked Snape to personally kill him when the time was right to:
-Prevent Draco from having to commit murder.
-Ensure that Snape enters Voldemort's inner circle easily (he was still not trusted well since he was a teacher at Hogwarts)
-As a side bonus, Dumbledore would be saved from the slow and painful death the curse would cause in the future.