There are several explanations, both in and out of universe:

• The Nazgul (more specifically their fell beasts) would have been able to take them out.
• Anything flying into Mordor, especially a rarely-seen Giant Eagle, would be quickly spotted by Sauron, who would immediately muster every force he had around and in Mount Doom. Frodo and Sam were specifically trying to avoid the Eye's gaze.
• If the Eagle (or whomever was riding it) missed dropping/throwing the Ring directly into the fires of Mount Doom, they'd be handing the Ring directly to Sauron's forces.
• Tolkien mentioned in notes and conversations that he did not want the eagles to be seen as "Middle-earth taxis". They thus intervene directly only in times of great need, as the last option.

There are several explanations, both in and out of universe:

• The Nazgûl (more specifically their fell beasts) would have been able to take them out.
• Anything flying into Mordor, especially a rarely-seen Giant Eagle, would be quickly spotted by Sauron, who would immediately muster every force he had around and in Mount Doom. Frodo and Sam were specifically trying to avoid the Eye's gaze.
• If the Eagle (or whomever was riding it) missed dropping/throwing the Ring directly into the fires of Mount Doom, they'd be handing the Ring directly to Sauron's forces.
• Tolkien mentioned in notes and conversations that he did not want the eagles to be seen as "Middle-earth taxis". They thus intervene directly only in times of great need, as the last option.

There are several explanations, both in and out of universe:

• The Nazghul (more specifically their fell beasts) would have been able to take them out.
• Anything flying into Mordor, especially a rarely-seen giant eagle, would be quickly spotted by Sauron, who would immediately muster every force he had around and in Mount Doom. Frodo and Sam were specifically trying to avoid the Eye's gaze.
• If the eagle (or whomever was riding it) missed dropping/throwing the Ring directly into the fires of Mount Doom, they'd be handing the Ring directly to Sauron's forces.
• Tolkien mentioned in notes and conversations that he did not want the eagles to be seen as "Middle Earth taxis". They thus intervene directly only in times of great need, as the last option.

There are several explanations, both in and out of universe:

• The Nazgul (more specifically their fell beasts) would have been able to take them out.
• Anything flying into Mordor, especially a rarely-seen Giant Eagle, would be quickly spotted by Sauron, who would immediately muster every force he had around and in Mount Doom. Frodo and Sam were specifically trying to avoid the Eye's gaze.
• If the Eagle (or whomever was riding it) missed dropping/throwing the Ring directly into the fires of Mount Doom, they'd be handing the Ring directly to Sauron's forces.
• Tolkien mentioned in notes and conversations that he did not want the eagles to be seen as "Middle-earth taxis". They thus intervene directly only in times of great need, as the last option.