My Illogical Theory
Albeit a great answer has already been made, I want to say my reasons.
I believe that Audino didn't get the Fairy-type firstly because of it's main gimmick - it's EXP. yield. Pokemon like Ditto and Smeargle don't have a special type, all they have is the Normal-type. But they have a very special gimmick, Ditto being able to transform into every type, and Smeargle being able to legally learn every move in the game. (Of course, Mew is an exception 'cos it's legendary.) Audino doesn't really have much of a use as a team member really, it's only a game gimmick to help grinding.
My second reasoning is the fact that it would have been redundant keeping Audino a Normal-type for one generation. This is a bit of a weaker point, but it's still true. Audino had only just been introduced into the Pokemon world, and it would seem stupid to add another type to it the next generation. Think, no Gen V Pokemon got Fairy-typed in Gen VI. With that, it would just be strange to randomly add another type to it in ORAS, but not in XY, two Gen VI games, hence the Fairy-type Mega Evolution. Audino definitely deserves a Fairy-type, I agree.
Also, according to this, Audino seems to be based on a rabbit. I'm pretty sure rabbits go under the 'Normal' category.
But of course, it was all Game Freak's choice. Though those are just a few points that can quench your curiosity.
Hope I helped. :)