well mostly it’s explained by the fact that it didn’t happen.

"In rode the Lord of the Nazgûl, under the archway that no enemy ever yet had passed, and all fled before his face.

All save one. There waiting, silent and still in the space before the Gate, sat Gandalf upon Shadowfax: Shadowfax who alone among the free horses of the earth endured the terror, unmoving, steadfast as a graven image in Rath Dínen.

‘You cannot enter here,’ said Gandalf, and the huge shadow halted. ‘Go back to the abyss prepared for you! Go back! Fall into the nothingness that awaits you and your Master. Go!’

The Black Rider flung back his hood, and behold! he had a kingly crown; and yet upon no head visible was it set. The red fires shone between it and the mantled shoulders vast and dark. From a mouth unseen there came a deadly laughter.

‘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 then the Rohirrim arrive and the Rider leaves.

Because Gandalf was a man, and the plot demanded it, perhaps?

The Black Rider flung back his hood, and behold! he had a kingly crown; and yet upon no head visible was it set.

I remember the chills I got when I read it for the first time.

I’ll be mad till my last breath at Peter Jackson for not including this in the movies.

The sense is that Gandalf seemed too powerful and the director decided to humble him a bit to add tension.

The answer is pretty simple:

Peter Jackson isn’t nearly as good at telling a consistent story as Tolkien was. This scene isn’t in the books.

Have to watch the Rankin Bass version for that!

I wouldn’t say that. I’d say he did a great job adapting text to a visual medium. In the text just having the sword light on fire in preparation works. When you see it played out, everyone is going to ask why he didn’t take a swing before leaving.

This is exactly what the previous comment is saying. Jackson changed stuff for the movies to cater to mainstream movie audience expectations, at the cost of the worldbuilding and lore.

Maybe having a guy that’s totally invulnerable to the most powerful bad guys is actually not great world building in the first place.

Maybe having a guy that’s totally invulnerable to the most powerful bad guys is actually not great world building in the first place.

He’s not at all invulnerable, in the book they were about to throw down and the Witch King was pretty confident about his chances. Also Gandalf literally gets killed by the Balrog. And beaten and imprisoned by Saruman.

well mostly it’s explained by the fact that it didn’t happen.

"In rode the Lord of the Nazgûl, under the archway that no enemy ever yet had passed, and all fled before his face.

All save one. There waiting, silent and still in the space before the Gate, sat Gandalf upon Shadowfax: Shadowfax who alone among the free horses of the earth endured the terror, unmoving, steadfast as a graven image in Rath Dínen.

‘You cannot enter here,’ said Gandalf, and the huge shadow halted. ‘Go back to the abyss prepared for you! Go back! Fall into the nothingness that awaits you and your Master. Go!’

The Black Rider flung back his hood, and behold! he had a kingly crown; and yet upon no head visible was it set. The red fires shone between it and the mantled shoulders vast and dark. From a mouth unseen there came a deadly laughter.

‘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 then the Rohirrim arrive and the Rider leaves.

Yes pre-super Saiyan Gandalf is weaker.

He’s not at all invulnerable, in the book they were about to throw down and the Witch King was pretty confident about his chances. Also Gandalf literally gets killed by the Balrog. And beaten and imprisoned by Saruman.

He literally is not a man.

The Witch King was still gonna go him.