When you fall for more than one block with a parrot on your shoulder, the parrot is supposed to come off, but it doesn't seem to apply to elytras. This is what happens when you fly up in Creative and glide with an elytra while a tamed parrot is on your shoulder.
Expected result: You're technically still falling, and you're moving really fast to boot, so the parrot should be whipped off your shoulder.
Bug: The parrot hovers in the air where your shoulder would normally be, as can be seen in third person. Oddly enough, the view in the upper left shows it on your shoulder, even though you can go horizontal.
How to reproduce:

1. Go into Creative mode, equip an elytra, and spawn a parrot.

2. Tame it with some seeds and let it sit on your shoulder.

3. Fly up to a decent height (the parrot should still be on your shoulder), stop flying, and immediately start gliding with the elytra.
You get something like this: