I was looking for an arceus in the GTS and came across a lvl100 shiny arceus holding a masterball and was requesting a mew so I was all like OMG IM GOANA GET AN OP ARCEUS (even though I beat a hacked arceus with a mew rest/sleep talk combo) but then it said "This is a special Pokemon! You cannot trade it!" and I was all like WHAT THE HECK!!! and accidentally knocked over my laptop.
It has certain ribbons attached to Mew, which makes it a "special Pokemon". So unless you get a mew with no event ribbons, you cannot trade it on the gts.