Fae (the name for fairy creatures) and dragons are both mythical creatures.
Fae are normally cunning creatures. Clever, quick on their wings, and firing supersonic magic bolts at big, bulky dragons ensures them victory against said Dragons. Dragons cannot hit fae due to their ability to use magic barriers, their size (sprites, at least) and their speed.
Much of the folklore about fairies revolves around protection from their malice, by such means as cold iron (iron is like poison to fairies, and they will not go near it) or charms of rowan and herbs, or avoiding offense by shunning locations known to be theirs. (Source)
This explains their weakness against Steel, and charms can be used with poisonous herbs, explaining the weakness to Poison.
Also, Dragon Types needed a nerf. They had a weakness of one of the rarest types in the game (Ice), and a weakness against themself (which was rarely exploited).
Source: Experience with Myths