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Closely related: Could the Horcruxes be destroyed with Avada Kedavra?
Also closely related: Fiendfyre to destroy Horcrux
At one point, Hermione discovers that the only way to destroy a horcrux is to damage is beyond any possible magical repair (e.g. Basilisk venom, a killing curse, fiendfyre, or the Sword of Gryffindor given the fact that it had been exposed to Baslisk venom).
Apparently, the only one of those possibilities that they seriously considered was somehow retrieving the Sword of Gryffindor, which seemed like a long shot at best.
In fact, the only reason that they retrieved it at all is that Snape gave it to them. Neville also obviously later pulled it out of the sorting hat at the Battle of Hogwarts to kill Voldemort's snake Nagini, who was the final horcrux.
Apparently, a killing curse is rather difficult to cast, but Harry's able to cast the other two unforgiveable curses successfully, and I doubt that using a killing curse on a Horcrux would damage your soul in the same way that killing an actual person would.
Apparently, they were afraid to use fiendfyre given how dangerous it is and how easily it could go wrong.
Why didn't they figure out how to cast one of those spells, take it to someone who already knew them, or imperius or otherwise coerce a Death Eater to destroy it for them?