Hawlucha is just a guy in a bird suit, notice how the beak and his mouth are not actually the same body part? --- 3DS Friend Code: 0344-9443-2457, Newtown Dream Address (AC:NL): 5400-2162-1014 "Do you have the courage to ride with the devil?"
The real reason is that GF got lazy. All of the pokemon that can attend Sky Battles are always flying / hovering above the ground. Even Xatu is flying above the ground... while maintaining its signature totem pose, which looks ridiculous. Pokemon that put their feet on the ground cannot attend Sky Battles, even if they're Flying type or have Levitate.
Examples include Hawlucha, who's a Flying type that can learn Fly, and Gengar, who has Levitate and evolves from Gastly and Haunter, both of which also have Levitate and CAN attend a Sky Battle.
The entire reason why certain pokemon who SHOULD be able to attend a Sky Battle can't is because Gamefreak decided to use only one idle animation, and didn't bother giving them a flying / levitating animation. --- 3DS Friend Code: 5043 1777 9788 Safari pokemon: Grumpig, Girafarig, Woboffet. PM me if you add me.