Why does Guan Yin ride a dragon?
Wikipedia says that she is "protector of fishermen, sailors, and generally people who are out at sea".

A Chinese dragon is esteemed (a symbol of the emperor), and "traditionally symbolize potent and auspicious powers, particularly control over water, rainfall, typhoons, and floods", also prosperity and good luck and so on, rulers of weather and water.

So I assume that riding a dragon like that symbolizes control over the sea (part of being "protector of fishermen and sailors").