Well, I can't promise to clear up anything. This is one of the most hotly debated topics in Tolkien fandom. The fact it is STILL hotly debated after 55 years indicates Tolkien never really provided us with a clear answer, if I understand what the issue is (the thread has drifted all over the place, from what I can tell).

Let's look at the prophecy again:

  "But it is said that when all was lost suddenly the Witch-king
  himself appeared, black-robed and black-masked upon a black
  horse.  Fear fell upon all who beheld him; but he singled out
  the Captain of Gondor for the fullness of his hatred, and with
  a terrible cry he rode straight upon him.  Earnür would
  have withstood him; but his horse could not endure that onset,
  and it swerved and bore him far away before he could master it.



  "Then the Witch-king laughed, and none that heard it ever
  forgot the horror of that cry.  But Glorfindel rode up then
  on his white horse, and in the midst of his laughter the
  Witch-king turned to flight and passed into the shadows.  For
  night came down on the battlefield, and he was lost, and none
  saw whither he went.



  "Earnür now rode back, but Glorfindel, looking into the
  gathering dark, said: 'Do not pursue him!  He will not return
  to this land.  Far off yet is his doom, and not by the hand
  of man will he fall.'  These words many remembered; but
  Earnür was angry, desiring only to be avenged for his
  disgrace."
  (From "Appendix A" in The Return of the King)

Gandalf makes reference to the prophecy in "The Siege of Gondor":

  "'Yet now under the Lord of Barad-dur the most fell of all his
  captains is already master of yoru outer walls,' said Gandalf.
  'King of Angmar long ago, Sorceror, Ringwraith, Lord of the
  Nazgul, a spear of terror in the hand of Sauron, shadow of
  despair.'



  "'Then, Mithrandir, you had a foe to match you,' said Denethor.
  'For myself, I have long known who is the chief captain of the
  hosts of the Dark Tower.  Is this all that you have returned
  to say?  Or can it be that you have withdrawn because you were
  overmatched?'



  "Pippin trembled, fearing that Gandalf would be stung to sudden
  wrath, but his fear was needless.  'It might be so,' Gandalf
  answered softly.  'But our trial of strength is not yet come.
  And if words spoken of old be true, not by the hand of man
  shall he fall, and hidden from the Wise is the doom that awaits
  him....'"

The Wise, according to Tolkien in some passages, were usually the Elven-lords -- particularly lords of the Eldar. Sometimes he seems to have included the Istari among them. So, Glorfindel would be one of the Wise. Gandalf therefore implies that even Glorfindel did not know exactly how the Witch-king's end would be brought about.

Based on that, I would say that Glorfindel knew the Witch-king would not be slain by Earnür or any man, a male soldier or warrior. He could not be certain of anything else, not being able to see the end of the Lord of the Nazgul. So Glorfindel should not have known that a woman would strike the killing blow.

Now, what does that have to do with who could kill the Nazgul? Absolutely nothing, so far as I can determine. It required two sword-strokes to do away with him: Merry's sword had to "deal that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit its unseen sinews to his will."

After Merry broke whatever this spell was which protected the Nazgul from serious harm, Eowyn stabbed him in the face. She struck the killing blow (Tolkien affirms this much somewhere although the reference escapes me -- if someone insists, I'll try to find the passage in the next few days).

In any event, Merry's sword was special. The same passage I cite above from "The Battle of the Pelennor Fields" says that "no other blade, not though mightier hands had wielded it, would have dealt...." We know from when Aragorn, Gimli, and Legolas recover Pippin and Merry's swords in "The Departure of Boromir" that the Barrow blades have spells on them "for the bane of Mordor" according to Aragorn, which the Orcs recognized or sense -- hence they left them when they plundered the Hobbits.

On Usenet it was recently argued that these four blades might not have been anything special -- after all, why should Merry's sword be singled out by Tolkien in the later passage? Well, I've had some time to think about this one. :)

I believe that Merry's blade was unique in that battle. Frodo's Barrow blade had been destroyed at the Ford of Bruinen, and he now carried Sting. Sam's was with him (or lost, plundered by the Orcs of Cirith Ungol at this point). Pippin still had his sword but he was up in the city leading Gandalf to Denethor's pyre.

Also, the barrow from which Tom Bombadil took the blades seems to be that of the last prince of Cardolan -- so the story strongly implies. His grave goods may have included treasure gathered by the Wight through the centuries, but it seems to me Tom knew the Hobbits needed special weapons to help them against the Nazgul. He claimed not to be a "master of Riders from the Black Land far frmo his country."

But he was very, very well-versed with the history of the Dunedain. He had told the Hobbits stories of the old kingdoms while they stayed with him, and he remembered fondly some ancient woman who had worn the brooch he picked out of the Wight's treasure for Goldberry. Also, Tom knew Aragorn (or knew of him, though Aragorn also knew who Tom was). So he probably knew the swords had spells upon them, or could at least tell they must have some sort of power about them.

Hence, I think Tom intentionally picked out weapons which could benefit the Hobbits against the Nazgul. But he didn't bother to tell them what he had given them. I don't understand this part of the story, but he seems too intelligent, too aware of what had happened in that land centuries before, too not recognize those swords for what they were.

Therefore, I believe that Merry's sword was required for bringing about the end of the Nazgul. It was, in fact, only a long knife to a Dunadan, but it might have (along with the other three blades) represented the finest work of some ancient Dunadan smith who died in the final onslought against Cardolan in 1409, or even earlier. With the death of the prince himself, apparent owner of the four knives, they vanished from knowledge and history. No one knew that weapons which could be used against the Nazgul existed.

So, Glorfindel himself probably did not know such weapons had been made -- or, if he did, then he must have known by 1975 that they had been lost. Certainly no one was carrying them around. It thus follows that even if Glorfindel could somehow foresee that one of the Barrow blades would be used against the Nazgul, he must not have seen who would use the weapon. And because the blade did not actually kill the Nazgul, if it figured at all in Glorfindel's foresight, it could not reveal the manner of the Nazgul's death to him.

All of which is to say, more-or-less, that anyone wielding one of those Barrow blades (or similar weapons, if indeed there were others of like nature) should have been able to break down the magical defenses of the Nazgul and render them vulnerable to the strong blow of a normal blade.

I find it doubtful that the Dunadan weapon smith who made the Barrow blades would have intended for Hobbits to wield them in battle against the Nazgul.

So, I think that addresses the issue at hand, but I can't say it really provides any answer. I don't believe Glorfindel knew that a woman would strike the killing blow -- it sounds to me as though he had a sense of something other than a man such as Earnü would be involved in killing the Lord of the Nazgul, but the Elf could not see clearly because (perhaps) the deed would be effected by two people, neither one of them a "man" as he would have thought of a man.

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Parma Endorion: Essays on Middle-earth, Revised Edition