It didn't matter what the type was called, it was going to be super effective against the Dragon type (and immune to it, it seems). The fact that the Fairy type could be easily applied to previous-gen Pokemon to quickly let it play catch-up to the rest of the types would have been a plus for GameFreak.
Ever see Cinderella? The climax involved a magic sword enchanted by fairies and a dragon slain by said sword.
To be fair, the dragon was also a fairy. And it was sleeping beauty.
Of course, in Dungeons and Dragons (and The Fairly Oddparents, as a D&D shout-out), dragons are actually resistant to magic.
But ultimately it comes down to the fact that dragons and fairies are both mythical, magical creatures. There had to be some relationship between them, and since Dragon-type has become overpowered lately, that relationship should give Fairy the advantage.
Socran's Razor: "Never attribute to massive stupidity by someone else, what could be explained by a tiny bit of stupidity on your own part."