Note that "everyone is special" has a mutable meaning, and people aren't always clear in context which one they mean. In a lot of religious or philosophical traditions, it boils down to: "Worthy of respect as a human being," or something very similar. That is, by virtue of being human and not, say, a rock or a turnip, you classify in the "special" category.
Then there is the more modern conception of, "everyone has some special, super, stupdendous thing that they contribute that is unique to their personality in its own special way." I've tried to make a neutral rendering of that version, but am not sure that I quite succeeded. This one is very much in dispute, with the counter-point being something like, "Most people are 'just folk' -- worthy of that inherent respect thereof, that being all that is needed to get it, but not likely to be heroic or any other 'special' quality that you care to name."
Two of the more common tropes explaining player character powers both side with the idea that everyone isn't special in that latter sense, albeit for different reasons:
1. PCs are called out as specifically special is usually saying that they have something beyond that inherent dignity that marks them--fate, favored by the gods, whatever.
2. PCs are like everyone else, but eventually are special by what they learn, do, and become. Other people might have been special, but aren't.