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>Why is there only 1 (one) pure flying-type?
Flying is treated as a combination of Wind/"Birds or creatures that fly" type. With moves like Wing Attack, Gust, Peck, Feather Dance, Air Cutter, Air Slash and etc.
Tornadus only normally learns moves on the "Wind" side and is a symbol of the wind itself. The Wind side can exist on its own as one type but the Flight-based side usually has to coexist with another type.
>And why is there only 1 line with flying-type as their primary type?
Considering the Pokemon in question are Noibat and Noivern, I assume that just has to do with how Wyverns are treated in fantasy games.
Usually they're always seen as "not true dragons" so for some autistic, it's Flying/Dragon instead of just Dragon/Flying because that'd be an insult to the true Dragon Pokemon.