I'm going to copy/paste my response to a similar comment:

You know, people underestimate how difficult it is to grab a goose that's flapping and pecking at your head

You can't keep your eyes open, unless you just enjoy having them poked by feathers or beaks. That isn't about pain, it's about the reality of eye injury being a very bad thing.

There's tricks we used in jujutsu that make use of that reflex. You make fast movements towards the eyes, particularly if you can get close enough to make air hit the eyes from the movement, and the eyes are closing, period. You can be ready for it, watching it come, and you'll still at least blink. It isn't voluntary.

Sure, you could stand there with your eyes closed, waiting for a chance to grab the bird that's battering you. It isn't going to kill you, it can't unless it gets really lucky and catches your carotid just right. But, while you're groping for that neck, you're getting your face bruised and scratched up. Punching or slapping doesn't do anything because they just move with it.

So, it's easier to give the bird what it wants: you away from its nest.