Dr. Loye Miller (1918) published the following account, as given to him by one of his students:
Last summer while my father and I were extracting honey at the apiary about a mile southeast of Thacher School, Ojai, California, we noticed a golden eagle teaching its young one to fly. It was about ten o’clock. The mother started from the nest in the crags, and roughly handling the young one, she allowed him to drop, I should say, about ninety feet, then she would swoop down under him, wings spread, and he would alight on her back. She would soar to the top of the range with him and repeat the process. One time she waited perhaps fifteen minutes between flights. I should say the farthest she let him fall was 150 feet.
My father and I watched this, spellbound, for over an hour. I do not know whether the young one gained confidence by this method or not. A few days later father and I rode to the cliff and out on Overhanging Rock. The eagle’s nest was empty. (Miss F.E. Shuman)
Deuteronomy 32:11-12 says this:
As an eagle stirs up its nest,
Hovers over its young,
Spreading out its wings, taking them up,
Carrying them on its wings,
12 So the Lord alone led him,
And there was no foreign god with him.
In Exodus 19:4 God says this:
4 ‘You have seen what I did to the Egyptians, and how I bore you on eagles’ wings and brought you to Myself.’
Some other good commentary on the subject can be found here.