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Both water and flying are the most common types and easily get slapped on every pokemon out there, which may lead to annoying situations like with Charizard not being dragon (inb4 genwunners). So my proposal is twofold, first allow pokemons to have three (3) types and to split water into fish and aquatic, while splitting flying into bird and aerial.
Fish would be used for deep-sea/fish based pokemon, while aquatic would be used for other water pokemon. Bird would be used for bird based pokemon, while aerial would be used for other flying pokemon.