Dumbledore took Harry along with him to the sea cave where the locket Horcrux was hidden because he felt Harry had earned the right to accompany him. However, why did Dumbledore neglect to bring the Sword of Gryffindor with him to destroy the Horcrux?
First, Dumbledore was sure he had found where the locket Horcrux was hidden -- in the sea cave. He did not know how it was protected or what kind of enchantments it had placed on it. Second, Dumbledore knew for certain by this time that the Sword of Gryffindor could destroy Horcruxes, for he himself used it to destroy Marvolo Gaunt's ring, plus he had arranged to leave the sword to Harry in his will by this time for the purpose of Harry using it to destroy Horcruxes. Third, Dumbledore had no way of knowing beforehand that the Horcrux in the sea cave was a fake, and that he would not need to actually destroy it. Finally, Dumbledore put Harry's life in great jeopardy by taking him along to the sea cave to begin with -- why not bring along the sword for extra magical protection? After all, Dumbledore had no idea how this Horcrux would react, whether it was cursed, poisonous, etc.
To have access to a rare magical object which could absolutely, one-hundred-percent destroy Horcruxes, and to not take it on a Horcrux-hunting mission, is so inexplicable.
Why did Dumbledore do this? Why did he leave the Sword of Gryffindor behind on the night he and Harry went to the sea cave to recover the locket Horcrux?
Please no answers sourced solely from the HP Wiki/Wikia -- answers based in canon or speculative answers based in the spirit of canon are welcome.