I can think of three possibilities why this may be happening:
1.) It is holding an item that cannot be traded
2.) It has a certain ribbon which prevents it from being traded
3.) It is from an event
"The player is not allowed to trade a Pokémon if it is holding a Mega Stone. Unlike in the past, event Pokémon that aren't holding event ribbons, such as Darkrai caught in Newmoon Island, cannot be traded anymore; attempting to do so will trigger the message "It's a special Pokémon. You can't trade it!"."
"Gift Ribbons available after Generation III normally prohibit Pokémon with them from being traded in the Global Terminal."
To check if your Pokémon has a Gift Ribbon click here.
"Starting from Generation II, items can be held by Pokémon when traded. The only items unable to be held by Pokémon, and therefore unable to be traded are key items, HMs, and, starting in Generation V, TMs."
Edit: It has a Premier Ribbon, a Premier Ribbon is a Gift Ribbon so that's why it won't let you trade it.
Hope I helped :)