Board Thread:General Discussion/@comment-24132296-20150405070433/@comment-26325447-20150802074442

Its not mentioned in the anime but in the LN, also posted in the wiki, " Kazuto resolved to never use Excalibur for personal gain as he believed that the sword contained the «caliber» of himself and his companions." The author,  Reki Kawahara, even stated that if Kirito was to use Excalibur in their duel, he would have had the advantage, which is just a big "what if" and nothing more seeing that Kirito would never use that sword for personal gain.