I know it is an old post, but here is my answer.
There is a much clear reason for Charizard not being the dragon type. Charizard's original Japanese name is Lizadon. It got that name because Lizadon's design was inspired by Radon(ラドン), a giant monster from Japanese Monster movie franchise.
Radon is a giant flying lizardlike monster which lives near a volcano. Since Lizadon(Charizard) took after its characteristics, it became fire type(volcano) and flying type since Radon's trait was all about flying with extreme speed. So since Radon, which inspired Charizard's design, was not a dragon at all, Charizard is also not a dragon. The mega evolution did add dragon type, but that is because many fans wanted Charizard to be a dragon type so Gamefreak granted that wish for a moment.
So the conclusion is, Charizard was not meant to be a dragon. Instead it was meant to be a giant flying volcanic lizard monster just like Radon. That is why it is fire flying type.