Why did Kirito toss the sword away in episode 17 of the second season? Towards the end of episode 17 (of the second season of SAO), after extricating Excaliber from the dais in the lowest level of Thrymheim, Kirito makes a comment about the sword "still being too heavy" for him. He then throws Excaliber away before jumping onto the flying tentacle-elephant.

Why did he do that? He doesn't seem averse to accepting the sword from Sinon a few minutes later (after she grabs the sword out of the air with one of her arrows), so it didn't seem like a "I am unworthy to wield this sword" type of thing.
It's because the sword was overburdening Kirito and since he can't put it into his inventory, he had to make a choice of either letting it go so he can make the jump onto Tonkii or going down with it:
From the (previously translated) light novel (Sword Art Online Volume 8, Early and Late, Caliber, page 308):

At that point, I noticed one terrible fact.
I couldn't jump.
To be more exact, in my arms was a heavy load the «Holy Sword Excaliber», so jumping five meters wouldn't be possible. Just by standing, my boots already bit into the ice.