Dragons are arrogant and possessive creatures, traits that can be used for either weal or woe. They consider themselves the first, most primal of creatures of the cosmos.
This arrogance tends to led them to be loners, or form groups of two to three at most. Because they are too perfect. A lone dragon is so powerful and self-sufficient that there's never a strong impulse towards subordinating themselves to a greater draconic society, making any attempt to form a species wide organization doomed to failure. In contrast, humanoid races are weak and imperfect so they have to suck it up and put aside their differences to cooperate and build civilizations.
All the dragons together could conquer the world, but dragons are so naturally asocial that it's impossible to get all the dragons to cooperate on one task like that. Thus each one individually becomes vulnerable to the cooperative efforts of the mortal races.
True dragons are also rare, and are not characterized by their colors, but by their actions. A majority of shadow or necromantic dragons may be considered evil, but it because of their nature, not the color of their scales when hatched.
Dragons normally consider giants, who also "claim" to be primal creatures, as rivals and enemies. The giants are also a proud race, full of hubris, which makes the antagonism somewhat mutual.
The entire cosmos could be considered the domain/possession of the dragons, and as such they are bitter enemeies of the Void, and those who would wield its corruptive power. Void Dragons are considered the vilest and most hated of traitors.