Before I begin, I'd like to inform you that this article is full of complicated Tolkien lore, that many people that haven't read the books or seen the movies will not understand. Not only that but there are also some minor spoilers to the story. If you are unfamiliar with Middle-Earth, proceed with caution. Instead I've linked another equally enjoyable article here.
Being the huge J R R Tolkien fan that I am, I of course had understood the upheaval about what is considered the greatest plot hole in the history of modern storytelling. In Tolkien's works we constantly see the great eagles of the Misty Mountains swoop down on the enemies in great times of need, like the incident with the Dwarves and the Goblins (The Hobbit), and the eagles flying in to aid the last ally of men to fight the combined forces of Sauron.
However, it doesn't take a genius to question why the eagles couldn't have flown The dwarves and Bilbo to Erebor, or why they didn't fly Frodo and the Ring all the way to Mordor and over Mt Doom.
Of course when I saw the title on reddit : "Lord of the Rings: A theory about the eagle 'plot hole'." I could't resist but read what this theory had to say. After reading the theory I felt truly astonished, and I've decided to write an article about it, because it hits it right on the noggin, and it's completely compatible with Tolkien's lore.
VulcanDeathGrip's Eagle Plot Hole Theory.
The entire theory revolves around the idea that Gandalf was planning to fly to Mt. Doom from the start. Of course he's no idiot, and with all of Middle-Earth at stake, he knew the Eagles would be willing to oblige.
As soon as Gandalf finds out that Frodo is indeed in possession of the One Ring, he sends Sam and Frodo to Bree, because he knows that the Nazgûl will be searching for them in the Shire. Gandalf then immediately rides for Isengard, where he counsels with Saruman what to do with the Ring. After Saruman reveals his true intentions of joining Sauron, Gandalf realises that he'll need to come up with a plan himself to destroy the Ring.
Using help from the Eagles, Gandalf is able to escape Orthanc. In the book/movie we are aware that Frodo and the Hobbits have teamed up with Aragorn, aka Strider, and have made it to Rivendell, where they meet Gandalf. As the audience you automatically assume that Gandalf rode the Eagle straight to Rivendell. That is not the case. Before going to Rivendell he met up with his Eagle friend Gwaihir, who happens to also be the Lord of the Eagles. There they discuss a plan Gandalf had been hatching atop Orthanc, which is to take the Ring to the Misty Mountains, and from there fly to Mordor. The plan of course must be kept an absolute secret, to prevent Sauron or Saruman getting hold of the plans and defending themselves appropriately. Gandalf for that reason tells no one in Rivendell. Not even Elrond.
As soon as Frodo has decided to take the Ring to Mordor, the Fellowship sets out to cross the Misty Mountains. Gandalf has planned to meet the Eagles on the East side, and the Redhorn pass/pass of Caradhras is the closest crossing to where they have planned to meet. However, Saruman has been watching the pass, and obstructs their passage, forcing them into going through the dark of Moria.
In Moria they are faced by a terrible accident. A Balrog of Morgoth. Before Gandalf falls into the chasm, he realises what a mistake he has made by not telling at least one of the others. All he is able to tell them in his last moments is the famous:
"Fly you fools."
The fellowship not understanding Gandalf's meaning, and misinterpreting it as 'Flee', they proceed to follow exactly what plan they were told. To walk to Mordor with the Ring. And that's exactly what they do.
After Gandalf fights the Balrog, and resurrects into Gandalf the white, we notice that Gandalf has forgotten a lot about his previous life, and he needs to be reminded of his old title by Aragorn when they meet him in Fangorn Forest. Of course he will have forgotten the entire plan to fly to Mordor, until when the plan renders itself useless. Luckily the Eagles swoop in at that last battle against the Orcs.
If you want to read the original Reddit you can do so here.