I am sorry I can't eat a hoopoe. I don't know what it is, but I would have enjoyed asking for it in the supermarket.
The categories for forbidden animals and fish are laid out in this sidrah but the criteria for birds is less clear. There are just lists of what can and cannot be eaten and the rabbis had to work out the connective factors.
It may be that all forbidden creatures embody some kind of characteristic that we are supposed to avoid. Hence animals that obtain food by wild means are not permitted and maybe the animals we can eat are more similar to humans than the ones forbidden to us. Even categories of fish could echo this idea: the fish we may eat live closer to us - to the surface of the water, and have fins and scales rather than shells, their swimming motion is forward-undulation rather than a sideways scramble on the bottom of the sea.
If we accept this idea, the list of permitted and forbidden birds makes more sense.