Draco to help Harry reform Slytherin House. And Harry to take as an enemy whoever Harry believed, in his best judgment as a rationalist, to have killed Narcissa Malfoy. If Narcissa had never gotten her own hands dirty, if indeed she'd been burned alive, if the killer hadn't been tricked - those were all the conditions Harry could remember making. He probably should've written it down, or better yet, never made a promise requiring that many caveats in the first place.
There were plausible outs, for the sort of person who'd take an out. Dumbledore hadn't actually confessed. He hadn't come right out and said he'd done it. There were plausible reasons for an actually-guilty Dumbledore to behave that way. But it was also what you'd expect to see, if someone else had burned Narcissa, and Dumbledore had taken credit.
And at what odds would you bet on that, said the Voice of Contrary Argument, if you had no personal stake in the issue? Uncertainty is no excuse for inaction. There's at least a substantial probability that Dumbledore killed her; shouldn't you take a quantitatively proportional step toward making him your enemy?
Harry shook his head, flattening one side of his hair and then another against the stone-tiled floor. There was still a final out, Draco could still release him from the oath at any time. He could, at least, describe the situation to Draco, and talk about options with him, when they met again. It didn't seem like a very likely prospect for release - but the idea of talking something over honestly was enough to satisfy the part of himself that demanded adherence to oaths. Even if it only meant delaying, it was better than taking a good man as an enemy.
But is Dumbledore a good man? asked the voice of Hufflepuff. If Dumbledore burned someone alive - wasn't the whole point that good people may kill, but never kill with suffering?
Maybe he killed her instantly, said Slytherin, and then lied to Lucius about the burning-alive part. But... if there was any possibility of the Death Eaters magically verifying how Narcissa died... and if being caught in a lie would've endangered Light-side families...
Be careful what we cleverly rationalize, warned Gryffindor.
You have to expect reputational effects on how other people treat you, said Hufflepuff. If you decide there's sufficient reason to burn a woman alive, one of the predictable side effects is that good people decide you've crossed the line and have to be stopped. Dumbledore should've expected that. He's got no right to complain.
Or maybe he expects us to be smarter, said Slytherin. Now that we know this much of the truth - no matter the exact details of the full story - can we really believe that Dumbledore is a terrible, terrible person who ought to be our enemy? In the middle of a horrible bloody war, Dumbledore set one enemy civilian on fire? That's only bad by the standards of comic books, not by any sort of realistic historical standard.
Harry stared up at the night sky, remembering history.
In real life, in real wars...