D&D Monsters: Red Dragons

Many medieval descriptions of dragons make no mention of them breathing fire, and this does not seem to be part of the original myths of the creatures. Nonetheless, the idea that dragons breathe flame does seem to have originated in medieval Europe, and is now de rigueur in fantasy depictions. It probably arose because of the association of evil dragons with hellfire, and the general idea of fire-breathing creatures certainly predates it (Leviathan breathes fire in The Book of Job, for example). 

In D&D, of course, it was originally decided that the five types of chromatic dragon should be distinguished by each having a unique attack, so that green dragons breathe poison, black dragons acid, and so on. Naturally, the most powerful of all the chromatic dragons was going to be the one that breathed fire, fitting the legends on which the broader idea is based.

D&D Monsters: Green Dragons

Medieval descriptions of dragons imply that they look rather like snakes, but they were said not to be venomous and, since they weren't always fire-breathing either, were often just very very strong. Some medieval bestiaries, for instance, describe dragons killing elephants by wrapping them up in their tail and squeezing like a constrictor. The poisonous counterpart of the dragon in medieval lore is the basilisk - which is basically just an incredibly deadly snake, much like the version in The Philosopher's Stone.

In D&D, the basilisk is quite a different creature, and very far from being legless. While the association of poison with serpentine beings make sense, it's not common in depictions of dragons. The D&D idea of certain dragons belching poisonous gas instead of something flammable is likely an original one - something added so that each of the five chromatic dragons had a unique attack mode. And in this case, of course, that's the green dragon, the mid-point in the five-point scale of increasing chromatic dragon power.