Why did Voldemort have to kill Harry *himself*?

[marthaforhp]

No: HPFGUIDX 173534

I've wondered about the answer to this question since near the end of 
HBP, when Snape roars to the fleeing Death Eaters to remember their 
orders and leave Potter to the Dark Lord.

And in DH, in Malfoy's Manor, Bellatrix doesn't simply kill Harry and 
be done with it.

Yet the original prophecy says nothing about who has to kill whom, 
only that neither can live if the other survives.

What have I missed?

Martha

PS  And I have looked in the Fantastic Posts for an answer.