Question: why does the sword of gryffindor kill horcruxes?
Answer: Could the Sword of Gryffindor have destroyed a horcrux before it absorbed the Basilisk Venom. As I recall Harry and Hermione figured out that the Sword of Gryffindor could be used to destroy a horcrux because it absorbed the Basilisk Venom. The sword absorbs anything that can make it stronger.