“When [he]Gandalf escapes on the eagle he doesn’t go directly to Rivendell to meet the hobbits, he first goes to meet the eagles… Gandalf and the eagles discus the plan for the eagles to take Frodo and the ring to Mordor and the eagles agree to do it, even though it could be dangerous for them because of the nine dragons the Nazgûl ride – the only things in Saurons defences that could stand in the eagles way…. Gandalf and the eagles agree that the plan should be kept very secret.
Being closest to the eagles the High pass would have been ideal for Gandalfs plan, but he decided against it because it was the obvious route …
The next most northern pass is what Gandalf settled for, even though it’s a very dangerous pass and even though it would mean a long journey north to meet the eagles, it is still the safest route for his plan to remain secret and that is all that’s important to him now. Keeping his plan secret was the main reason for him choosing the Redhorn pass. But Saruman was watching here too and sent storms to stop them. The Gap of Rohan would take them far too close to Isengard, and more importantly too far south. Which was no good for the plan as they’d have to travel the whole length of the Misty Mountains up the eastern side to meet the eagles. So the Gap wasn’t an option for Gandalf and the only way left was Moria. Which he didn’t like at all and we see he’s very reluctant. We think it’s only because of the Balrog but it’s also because of the risk of goblins and orcs seeing them go north on the eastern side (like the High pass) and because it was further south than he’d planned for which meant it would take longer to reach the eagles.
They almost get through Moria but Gandalf ends up fighting the Balrog and falling down the chasm. When he’s about to fall he realises he has to tell them the eagle plan quickly before he falls, and in a way that any nearby orcs and golbins won’t understand. He says ”Fly, you fools” hoping at least one of the fellowship understands what he really means… but they don’t. He falls and fights the Balrog.
Meanwhile the fellowship escapes Moria and carries on with the only plan they’ve known – get the ring to Mordor.Gandalf the Grey dies in the battle against the Balrog, but he comes back later as Gandalf the White. When he comes back he has forgotten a lot of things about his previous life. Even his own name, until he’s reminded of it when Aragorn calls him Gandalf. And he even forgot his plan to meet the eagles.
At the end when he needs to get Frodo and Sam away from the erupting Mount Doom he knows only one way to do it – calling the eagles to fly them out of there. This is when he remembers the plan, calling the eagles reminds him of it in the same way Aragorn calling him Gandalf reminded him of his name. But by this time the ring is destroyed and the plan is redundant.
TL;DR (I don’t blame you) Gandalf secretly planned on taking the fellowship to where the eagles live and having the eagles fly them to Mordor. The eagles lived on the other side of the Misty Mountains but all the routes for crossing them were too dangerous and difficult, and Gandalf (along with his secret plan) ends up falling down a chasm in a battle with the Balrog. Just before falling with the Balrog he tries to surreptitiously tell them the secret plan but was too surreptitious and they didn’t understand. When he came back as Gandalf the White he had forgotten many things, including the plan to meet the eagles.”