Here is the thing, Harry destroyed a Horcrux in his second year with a basilisk fang, even if he didn't know at the time. But in his sixth year, Dumbledore says to Harry, and I quote: "Horcruxes are difficult to find .. Even more difficult to destroy.", but then acknowledges that Riddle's diary was a Horcrux too.
So, why didn't Dumbledore just ask Harry how he destroyed it? Seeing as he was a wise old wizard, did that never pop into his mind? If he did, they would just have to go to the Chamber of Secrets again and pull out a tooth, like Ron and Hermione eventually did in the last one.
Dumbledore wouldn't have had to curse himself, and he wouldn't have had to die. Is Dumbledore really not that smart, or is there another reason?