Technically, we still have dragons in the scientific literature. There's the Komodo Dragon, the little gliding lizards in the genus Draco, big snakes, and a bunch of other things called dragons in one way or another. And that's not even touching dinosaurs.

But you are probably talking about the stereotypical 4 legs, wings, fire breathing dragon.

The thing is, dragons have diverged. Bestiaries from the middle ages and before are filled with mythologized accounts of real creatures. You've got Barnacle geese that grow on trees, salamanders that live in fire, and beavers that castrate themselves. Dragons show up here too, and the description is quite clearly of a big snake, probably and Indian Rock Python. The description itself is actually more accurate than what we have for some European animals in the same works.

You get dragons referred to as "Worms" and "serpents" all the way down through Tolkien, but they gradually pick up more legs and wings and breath. The modern dragon bears little resemblance to its serpent ancestor. But medieval descriptions of dragons match real world animals about as well as medieval descriptions of lions and leopards and geese and elephants match descriptions of real world animals. It just so happens that the modern idea of "dragon" somehow became separated from it's real world counterparts instead of becoming more identified with it.