False. The birds in the story do not go higher and higher in altitude
The story is about a young eagle who is different from the other eagles because he has a straight beak instead of a curved beak. He is ostracized by the other eagles and eventually leaves their nest to find his own place in the world. He travels to many different places, but he never goes higher and higher in altitude.
The phrase "birds of a different feather" is an idiom that means people who are different from each other. It doesn't typically refer to actual birds flying at higher altitudes. The birds in the story do not go higher and higher in altitude.