It might be more accurate to ask: "Why do we perceive creatures from so many different cultures as dragons?" Despite the perception that cultures around the globe have their own dragon myths, that's a bit misleading - they have their own monster myths, which many have conflated with the European label or image of dragons, even if the origins and attributes are very dissimilar - even in Europe, you've got a wide range of difference between the Langton Worm and the legends of St. George and the Dragon. A large part of this conflation of different mythological critters can be traced back to early explorers, who tried to fit newly-encountered legends into a more familiar context, and partially due to 20th-century academics who were keen on finding universal, underlying myths - The Evolution of the Dragon (1919) by G. Elliot Smith predates Joseph Campbell's more famous Hero with a Thousand Faces, but they share a similar idea in an underlying structure or basis for form of a myth - which sort of assumes a connection even when there isn't necessarily one. The idea of a "universality" of dragons in different cultures is still pushed in in academic works like David E. Jones' An Instinct for Dragons - which was criticized for falling into pretty much the exact same trap, of assuming a universality which only really exists if you insist on calling very different creatures from very different cultures as "dragons." As Daniel Ogden put it in Drakon: Dragon Myth and Serpent Cult in the Greek and Roman Worlds 25:

Whatever one may think of the biological and evolutionary aspects of this hypothesis, the collation of the historical and cultural data upon which it rests leave smuch to be desired. Jones's 'brain-dragon' iamge as compounded from raptor, serpent, and cat appears to owe much to the contemporary Western stereotype of what one might term the 'medieval' dragon. His consequent hunt for images that salute this type across a range of historical human cultures lacks rigour. As for the Graeco-Roman material, let us note that the creatures the ancients knew as drakontes or dracones (no other creature from antiquity appears to be a candidate for an instantiation of Jones's 'brain-drag') fit his type poorly.

So part of the issue is that there are a number of different creatures from different cultures which have been subsumed under the general heading "dragon" (or equivalent term) when translated into a European language context - the Aztec Quetzacoatl, the Lambton Wyrm, heraldic wyvern, the Chinese long, the Babylonian sirrush, Smok Wawelski, etc. are all sort of crowded together under the term "dragon" in English, despite having very different physical appearances, habits, supernatural correspondences, etc. And in certain contexts, this has proven very useful - mainly I'm thinking of fantasy fiction and roleplaying games, both of which have benefitted from easy categorization. Even Tolkien in his Silmarillion used the broad term "dragon" to refer to fire-drakes and cold-drakes, winged and wingless; roleplaying games like Dungeons & Dragons and Shadowrun which take inspiration from Tolkien often have many widely varied creatures which are all collected under the label of "dragons" - and in part, the use of a common term tends to lead people to exaggerate commonly-perceived attributes (scaly/serpentine/reptilian natures, flying, wings, etc.), even as they dismiss things like "Does it have wings? How many legs does it have (if any)? Is it good or evil?"

There's always room for discussion, but perhaps the section Here be dragons in our FAQ will answer your inquiry.