If you attack these birds, they will pick you up. As soon as he picks you up, stop attacking, or he will stop flying and you will have to fight him. When he dies, he will drop you, and it probably won't be from a safe height.
Good luck finding a place to get range on them; I had a hell of a time before I finally found a place on a ledge at Firewalkers' Path. They do dip low near the Celestial Court (the path to the west of it), but that area is generally pretty crowded and expect jerks to kill your bird as you pass sometimes.
These birds are required to access particular areas of the Isle. Let them pick you up and carry you to your destination, at which point you can attack them to be dropped.
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