You've hacked the Pokemon to be permanently mega
Theres an option in powersave to edit your Pokemon to being pernamently mega.
You have a shiny locked Pokemon thats shiny
For instance you have a shiny Zapdos from X and Y, but Zapdos is shiny locked.
You have a Pokemon that you genned in
This is your most likely problem. If you used to genning option (I.e. you have the dex no. of a Pokemon in your bag, in masterballs) and then you genned it in, the game will know it was hacked and wasn't optioned legitimately and so wont let you battle with it.
Basically when ORAS says you have a "Special Pokemon" its either saying you have an event exclusive Pokemon, or a hacked Pokemon.
I think you most likely have the last problem, if you genned it say, a hitmontop, it would have been genned in to the pokecentre delivery lady and she would have given you the hitmontop at level 10 with hiddenpower. If you did that, the game will say it was special and wont let you battle with it.