Three ways of explaining this:
-Economic reasons. Japan has the most to benefit from an expanded EEZ (fishers) and all the economies could use the natural resources. But I don't believe that is the primary reason for the disputes today. Any government taking unilateral action on taking an island is going to see their trade prospects shot, which reverses the benefits. On the other hand, nations are building infrastructure on islands they securely hold to exploit the area.
-Military reasons. This drives the South Sea dispute more than any others, since the countries want as much distance between land and foreign navies. But such worries wouldn't take place if not for...
-Political reasons, which I subscribe to as the main cause. The truth is in all the East Asian countries - whose politics, regardless of appearance, are all oligarchical and rife with factional struggles - there are groups who benefit from continuing the dispute/stonewalling. Meanwhile, central governments have to appease the nationalism to maintain the coalition which guarantees them authority.
Certainly East Asian politics is not dominated by regionalism or by any mass movement. The problem is the borders are not defined at all - the transformation of the area the nation-state system is very recent.