Not about the eagles I swear.

I'm watching Fellowship and something comes to mind. During the war with Sauron, when Elrond and Isildur were on Mount Doom, why didn't Elrond, seeing that Isildur had been corrupted by the ring, not just kill him or take it from him and throw it in himself?

Seems to me something of such monumental importance is worth the live of one person.

If there is a clearly-stated reason that I missed, please feel free to let the mocking commence.