Elfin Mischievous Humbug wrote:
The problem lies also lies with how Peter Jackson depicts the Eagles' rescues in both the trilogy and The Hobbit. In the trilogy, Gwaihir rescues Gandalf from Orthanc because he happens to passing by the area, not because he was summoned by Gandalf. Additionally, in The Hobbit, the eagles only happened to be in the area and decided to help out, and again, they were not summoned by Gandalf.
Did you miss the parts where Gandalf sends messages to the eagles via insects? (a moth and a butterfly, respectively)