Despite what it may look like, Anaxa is not eating a bird, nor eating a Pegasus. She did kill a bird, and she is indeed eating the feathers, but she has no interest in the meat.
 
The Dragonfly Hive build their nests in dense tree-tops, spinning silk cocoons for their shelters, eggs, and trapped prey. To produce this silk, they need to have a rather regular intake of keratin-rich substances, and birds just happen to be flying mouthfuls of keratin (feathers.)
 
Dragonfly Hive drones regularly down and kill birds for such uses. Despite the potential horror of what this might mean for feather-winged Pegasi, the Dragonfly Hive actually has no interest in devouring Pegasi wings. It isn’t because they are unpalatable to them, but simply because not devouring pegasi wings means that the hive will not be hunted down and wiped out by furious pegasi should a victim happen to be found.