either must die at the hand of the other, Contradiction or Clue?

[M.Clifford]

No: HPFGUIDX 139640

Something that has had my attention since my first read of HBP, is the
line from the prophecy that says either must die at the hand of the
other. The reason this bothers me is because Dumbledore claims that he
and Harry have both destroyed a piece of Voldemorts soul each, or at
least he seems to. And I question, how can Voldemort die at the hands
of two people? It contradicts the prophecy. 

Unless the hands of Harry and Dumbledore are some how connected in an
alternating either/other fashion as Voldemort/Harry, or Dumbledore has
not killed Voldemort's Ring piece of soul, or both, there is no way
that either must die at the hand of the other fits Dumbledores story
in its simplest sense. According to the prophecy, as far as I feel I
can ascertain, Voldemort can not die in a random haphazard manner
where anyone can have a go at his scattered bits, he must die by the
hand of *the other* of the *either*.

I thought I had it scooped earlier in the game but Jo shot me down
with confirmation of the Diary Horcrux piece of soul having been
entirely destroyed in COS. So I have gone back to the drawing board
since then to take another stab at it. 

So far I have a framework that looks like this.

Either can mean simply Harry or Voldemort, but Voldemort is in seven
peices, so either can also mean either of each of his seven pieces.

Assuming either refers to each of LV's seven pieces then they can only
die by the hand of the other. The other could be just Harry, or could
be another Horcrux, or again it could be both if Harry is a Horcrux.

Dumbledore can only kill Voldemorts ring piece of soul, therefore, if
he was one of either Harry or a Horcrux.

For anyone who can understand what I have just said, if you notice an
error, please correct me. 

While I wait for corrections and comments I will just go on with some
of the speculative ground I have covered based on this.

One theory is that Dumbledore became Voldemorts Horcrux, through
destroying the ring, and then *allowed* Voldemort to kill him via the
DADA curse - hence one piece of Voldemort kills the other, and
either/other is satisfied. 

Another theory is that it all *has* happened by Harry's hand, and that
is why DD got Harry to force feed him the potion which eventually was
the thing that killed him. Snape was simply asked to push him off the
tower, I cant figure out why though.

OK, there are some of dark places that the prophecy has lead me into
after HBP, now I think I will put up my umbrella and await the showers
of rotten tomatoes.

Valky