The legend of why Owl has big eyes is one of many traditional Haudenosaunee stories told from generation to generation. Here is one version.
The Creator was busy creating various animals. He was working on Rabbit, and Rabbit was saying: “I want nice long legs and long ears like a deer, and sharp fangs and claws like a panther.”
“I do them the way they want to be; I give them what they ask for,” said the Creator. He was working on Rabbit’s hind legs, making them long, the way Rabbit had ordered.
Owl, still unformed, was sitting on a tree nearby and waiting his turn. He was saying: “Whoo, whoo, I want a nice long neck like swan’s, and beautiful red feathers like Cardinal’s, and a nice long beak like Egret’s, and a nice crown of plumes like Heron’s. I want you to make me into the most beautiful, the fastest, most wonderful of all the birds.”
The Creator said: “Be quiet. Turn around and look in another direction. Even better, close your eyes. Don’t you know that no one is allowed to watch me work?” The Creator was just then making Rabbit’s ears very long, the way Rabbit wanted them.
Owl refused to do what the Creator said. “Whoo, whoo,” he replied, “nobody can forbid me to watch. Nobody can order me to close my eyes. I like watching you and watch I will.”
Then the Creator became angry. He grabbed Owl, pulling him down from his branch, stuffing his head deep into his body, shaking him until his eyes grew big with fright, pulling at his ears until they were sticking up at both sides of his head.
“There,” said the Creator, “that’ll teach you. Now you won’t be able to crane your neck to watch things you shouldn’t watch. Now you have big ears to listen when someone tells you what not to do. Now you have big eyes — but not so big that you can watch me, because you’ll be awake only at night, and I work by day. And your feathers won’t be red like Cardinal’s, but gray like this,” and the Creator rubbed Owl all over with mud, “as punishment for your disobedience.” So Owl flew off, pouting: “Whoo, whoo, whoo.”
Then the Creator turned back to finish Rabbit, but Rabbit had been so terrified by the Creator’s anger, even though it was not directed at him, that he ran off half-done. As a consequence, only Rabbit’s hind legs are long, and he has to hop about instead of walking and running. Also, because he took fright then, Rabbit has remained afraid of almost everything, and he never got the claws and fangs he asked for. Had he not run away then, Rabbit would have been an altogether different animal.
As for Owl, he remained as the Creator had shaped him in anger — with big eyes, a short neck, and ears sticking up on the sides of his head. On top of everything, he has to sleep during the day and come out only at night.