It's like this. You control half of a country. Your Rival controls the other half. Now you both announce to release your half to form a single country but who should rule? If you let your Rival decide, you can bet it's gonna be "his man" and thus in all future dealings, the country would be his ally. Your rival thinks the same way. Hence the dispute. So even if you WANT to be nice and leave it, how can you be sure that the guy who ends up ruling the place isn't your rival's man? So you have a huge reason in staying around and make sure nothing of the sort happens.

Conclusion: Divided States