Speaking only of the book: There is no evidence at all that the Witch-King could defeat Gandalf.
Gandalf describes their first meeting:
'I galloped to Weathertop like a gale, and I reached it before sundown on my second day from Bree-and [the Nazgul] were there before me. They drew away from me, for they felt the coming of my anger and they dared not face it while the Sun was in the sky. But they closed round at night, and I was besieged on the hill-top, in the old ring of Amon Sûl. I was hard put to it indeed: such light and flame cannot have been seen on Weathertop since the war-beacons of old.
Even when Gandalf was just the Grey at Weathertop, he successfully held off all nine Nazgul who dared not face [his anger] while the Sun was in the sky. He withdrew only when night came and their power increased. (Yes, he said he was hard-pressed. But "hard put to it" is not the same as "defeated". He withstood all Nine all night. He's not easy prey.) And note that at the gate of Minas Tirith, it's not night that is coming, but morning and the Sun.
Again, as G the Grey, he had defeated a Balrog, a being of great innate power -- the Nazgul were human sorcerers and even with Sauron lurking menacingly behind them, there's no reason to suppose they were more powerful.
Additionally, at Minas Tirith, he is Gandalf the White and more powerful than he was. There is no reason at all to suppose that the Witch-King could kill him, let alone quickly. Only a few months before he fought Gandalf all night with the other eight Nazgul at his side and failed to even injure him.
(To be sure, there is no reason to think that Gandalf could kill the Witch-King, even without the "No Man" prophecy. This isn't a game where the characters encounter each other, roll the dice, and see who wins.)
The book says:
'Old fool!' he said. 'Old fool! This is my hour. Do you not know Death when you see it? Die now and curse in vain!' And with that he lifted high his sword and flames ran down the blade.
Gandalf did not move. And in that very moment, away behind in some courtyard of the City, a cock crowed. Shrill and clear he crowed, reckoning nothing of wizardry or war, welcoming only the morning that in the sky far above the shadows of death was coming with the dawn.
Note that the only evidence that the W-K could defeat Gandalf was the W-K's own braggadocio. Did he believe it? Was he hoping to bluff Gandalf? Was he suddenly aware that Gandalf was more than he had expected and trying to buy time? We don't know. But we do know for sure that the Witch-King of Angmar, head of the Nazgul, undead sorcerer, is an untrustworthy source.
Had the Witch-King fought Gandalf, he might perhaps have won. But based on his experience a few months before, he would almost certainly have been engaged in a long and hard fight, which certainly would waste precious time (and as Jason Baker has noted, the W-K was needed elsewhere Right Now), and might well have resulted in his wounding or even anti-un-death (or whatever happens to Nazgul which are killed.) (I'd also note that there's no reason to think that the W-K knows for sure that Gandalf is classed, prophecy-wise, as a Man (and thus unable to kill him) and not as Wizard or Maiar.)
The evidence is clear: If the Witch-King with 8 others beside him could not defeat Gandalf the Grey in a whole night of fighting, there was no chance that by himself he could defeat Gandalf the White quickly -- if at all.
The only rational course of action was for the Witch-King to break off the action and try to rally his troops.