Why was Excalibur not used near the end of season 2? I just finished re-watching episode 18 of season 2 of Sword Art Online, and in the end, Kirito throws Excalibur into the pit and then Shinon catches it with a spell arrow. Then, once the quest is over, he gets the sword as a gift from Urðr for saving the land. In the next episodes we don't see him use it.

Why isn't he using it?
In SAO Wikia about Excalibur, there is some trivia mentioned, among which:


  Kazuto resolved to never use Excalibur for personal gain as he believed that the sword contained the «caliber» of himself and his companions.




As mentioned in the comments and in Alchemist's answer, Kirito used the sword when fighting off the guild to buy Asuna some time.