It was only mentioned that Chatot was a Flying-type, which led to the fandom jumping to the conclusion that since they said it was a Flying-type, it must be pure Flying. I remember saying back then that it would most likely be Normal/Flying like every other plain old Flying-type.
As for why it's the way it is, here's my theory. It's not just that there aren't any Flying types, if you look at the order of types (for example Graveler is Rock/Ground, while Rhyhorn is Ground/Rock), you'll notice that no Pokemon has Flying as its first type, except for Tornadus. Maybe in the beginning, they wanted Flying to be a purely secondary type, like an early version of an ability, so it was always tacked on as the second type. In the case of a Pokemon that was just plain old Flying, they made it a Normal-type with Flying added on. I guess in the 5th generation, they finally decided to make an exception for legendaries.