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In Harry Potter and the Order of the Phoenix chapter 36, we see Professor Dumbledore dueling with the Dark Lord in the Ministry of Magic. From their exchange, it seems that Professor Dumbledore is not fighting to kill.
‘You do not seek to kill me, Dumbledore?’ called Voldemort, his scarlet eyes narrowed over the top of the shield. ‘Above such brutality, are you?’
‘We both know that there are other ways of destroying a man, Tom,’ Dumbledore said calmly, continuing to walk towards Voldemort as though nothing had happened to interrupt his stroll up the hall. ‘Merely taking your life would not satisfy me, I admit –’
Why did Professor Dumbledore not try to kill the Dark Lord?
At that time, Professor Dumbledore may have suspected that the Dark Lord has another Horcrux, so he would not truly die, but only become a bodyless spirit. Even so, that would have been a huge setback to the Dark Lord’s plans, as evidenced from Professor Dumbledore’s explanation in Philosopher’s Stone chapter 17.
‘[… Voldemort] is still out there somewhere, perhaps looking for another body to share … not being truly alive, he cannot be killed. He left Quirrell to die; he shows just as little mercy to his followers as his enemies. Nevertheless, Harry, while you may only have delayed his return to power, it will merely take someone else who is prepared to fight what seems a losing battle next time – and if he is delayed again, and again, why, he may never return to power.’
This question may be a special case of Why should the Horcruxes be destroyed first?