Fighting = warriors
Psychic = mages, oracles
Dark = thieves, tricksters & assassins
normal = animals
Dragon = Monstrous mythical creatures such as hydra and dragons

with these thought in mind fairy works out well from what we've seen
>weak to Poison and Steel
Fairy folk are very strongly linked to the environment so pollution would be strong and steel is just unnatural
>immune to Dragon
the idea that a giant dragon would have a hard time catching a little agile fairy
>super effective against Dragon, Dark, Ice and Fighting
fairies are commonly seen punishing wrongdoers and warriors would have a hard time fighting a fairy
also Fairies Are associated with the spring thaw in many legends
>Fire and Psychic-type Pokemon take half damage from it
Mages would have a better understanding of magical creatures and could easily defend against them

the only thing I hope for now is that Grass is immune or at least resistant to it it could use the buff