Within the Pluto-Charon system, the center of mass it outside of Pluto, so because of this it can't be claimed that either object "truly" orbits the other, so therefore it must be considered a binary system, this implies that Charon is also a dwarf planet as well as Pluto, so it should not be considered a moon.
I looked up that double planet idea in Wikipedia. It makes sense, but hey my opinion is it's just a bit off the kilter moon. I also have the opinion that Pluto is a planet, just cause I like it that way. That's what I like about opinions, even when the odds look quite good that you are wrong in yours you can keep it anyway, just cause you like to (Talking about myself rather that you. I don't know much about astronomy). Although... I kind of wish I had paid attention to that Rick and Morty episode now.