if evolution had taken a different turn, could dragons have existed?

Dragons are a grand classic of fantasy. For this question, let's assume we're talking about the following stereotype:

what about the dragons depicted in myths and legends? Huge, winged, terrifying, fire-breathing beasts: could they ever have existed?

While no direct evidence has ever been discovered to support the prior existence of dragons, these mythical creatures are present in the legends and folklore of many countries across the world. 

So, is this a coincidence? Two distinct categories of dragon have been identified: the Chinese dragon and European dragon, with the former thought to have contributed to all dragon myths in Japan, Korea and other areas of East Asia.

 Most dragons, regardless of their origin, appear to have begun as serpentine ideas before becoming more elaborate in features, with wings and legs becoming common components. Not all of them breathe fire.

 In fact, some of them were believed to dwell in wells, lakes and other watery habitats.While there appear to be a fair number of fierce dragon fans dotted around the web  it's generally agreed that dragon myths must've arisen from a variety of creatures already in existence. 

One anthropologist, David E. Jones, even argues that the widespread belief in dragons is down to an evolutionarily embedded fear of three core predators in the human mind