There are many disputes that appear pointless in my eyes. These are disputes that seem to have an easy resolution, but which the countries involved continue to fight over.
A couple examples:
Taiwan and China. Taiwan is now its own country. It has a different form of government and Beijing doesn't really have a say in its internal affairs. Compared to Taiwan, mainland China is huge. Why don't they just agree to go their own way? If China really believed that Taiwan was still part of China, they would have invaded a long time ago. A huge country such as China would not allow a group to claim sovereignty of an island inside their country.
South Korea and Japan over the Liancourt Rocks. This is even more pointless than the Taiwan/China issue. The rocks are uninhabited and practically useless. Why can't one country just give them up or come to an agreement on them being "international"?
North Korea and South Korea. Why can't North Korea be recognized as a sovereign country? It has been over 50 years since the Korean War. Yes, technically it didn't end, but in reality it's over. If large-scale fighting broke out, no one would call is just the "Korean War". Most likely it would be the "Second Korean War".
What reason would a country have for keeping these disputes open?