What species of eagle pushes their young to teach them flying?
There are many references to eagle pushing their young off the nest to make them know how to fly, for example this motivational video.
It is also described in this website:
Let me show you "the ways of an eagle" in the nest, and give you a picture of our lives as well. After the eaglets get to a certain size, or maturity, everything changes! One day the mother eagle comes back from being gone, but this time there’s no food in her beak, and she doesn’t land on the edge of the nest. Instead, she hovers over the nest.
You may not know this, but an eagle can do almost what a hummingbird can do. Even though they are great birds, they can remain almost motionless in midair with those great wings just undulating in the breeze. They do this about three feet above the nest. I’m sure if little eagles could talk to one another—and maybe they can—one would certainly say, "My, what strong wings Mommy has."
Why does the mother do this? She is demonstrating that those curious appendages on the babies’ backs have a useful function. Eagles, of course, were meant to fly, but they don’t know that. If we take an eagle and separate it at birth from its parents, it will never learn to fly. It will just grovel around in the dirt like a chicken. It might even look up and see eagles soaring overhead and never guess that it was meant to soar in the heavens.
Eagles have to be taught, and that’s the mother’s job. So first she just demonstrates.
The next thing she does is come down into the nest and surprise her young. One can imagine how warm it must normally be for the little eagles to snuggle with their mother and be enshrouded with her feathers, but this time she puts her head up against one of the little ones, and pushes that little one closer and closer to the edge of the nest. ("Hey mom, mom, what are you doing?")
All at once she pushes the little one out of the nest, and the eaglet falls down the face of the cliff, surely to be destroyed. 323
But not so! In a flash the great mother eagle flies down, catches the little one on her back, and flies up and deposits it in the nest. ("Whew! Mom, that must have been an accident.") But it wasn’t an accident. The mother bird pushes the little one out again, and again, over and over.
Why would a mother do that to her young? Does she hates the little one? Not at all. It’s just that those little birds were made to fly, and they don’t know it, so she is going to push them out of the nest. She never lets them hit bottom, but she does let them fall, because they have to learn something they don’t know.
The next time the mother bird comes back she decides to clean house, and so she stands on the edge of the nest. The first things to go are the feathers inside; she drops them over the edge. Then the leaves go over the edge—heave ho! While this is going on, she’s not very talkative, either. ("Mom, what are you doing?") She pays no attention. Since she built the house, she knows how to take it apart.
Next she decides to take the sticks out of the middle of the nest, and with her great strong beak and feet, she’s able to break them off and stand them straight up. ("<PERSON>, it’s not comfortable in here anymore.") Then she takes certain key sticks out of the nest and throws them over the edge. ("What are you doing, Mom? You are wrecking my room.")
She seemingly pays no attention to the concerns of her young as she prepares to pull the nest apart, for she is determined that those little ones will fly, and she knows something they don’t. She knows they will never fly as long as they remain in the nest.
However, looking at this very interesting documentary on white-tailed eagle, the young eagles don't learn to fly by getting pushed as described in the motivational video, but they learned flying by practicing their wings on good winds.
Looking from the nesting place (cliff), I read that it might be Golden Eagle. But the section describing the fledgling doesn't say anything about the parent eagle pushing the young, although it does say about "jumping off":
The first attempted flight departure can be abrupt, with the young jumping off and using a series of short, stiff wing-beats to glide downward or being blown out of nest while wing-flapping. 323