The bold statements above can be easily proven, but to do so, the concept of a winnable versus an unwinnable war needs to be established. And in order to do that, we must first define war itself. Dictionary.com has a very useful definition for the word:
1. a conflict carried on by force of arms, as between nations or between parties within a nation; warfare, as by land, sea, or air.
2. a state or period of armed hostility or active military operations: The two nations were at war with each other.
3. a contest carried on by force of arms, as in a series of battles or campaigns: the War of 1812.
What is paramount in the above is that a war is entered into by nations or by groups competing for the same goal. Throughout history we can see wars between empires competing for geographical space, or between groups of people competing for their control or sovereignty. In the case of the United States, the Revolutionary War was over the sovereignty of their inhabited area of the New World. The War of 1812 was actually between France and England, but spilled over into the New World and, thus, affected the new nation in that way.
Likewise, we can see how the Civil War was between two competing ideals over certain rights and the sovereignty of the people who believed in those rights. The Mexican-American War was over territory. The first and second world wars were waged between two separate ideologies and their sovereignty over the peoples affected. They were also about geographic control of strategic areas needed to maintain such ideologies. But in all cases, the goals on both sides were equivalent, maintain or obtain the geographic areas in question, or change the control and sovereignty of the people affected in those areas. Both sides had equivalent stakes in the outcome and the goals could be mutually contrasted.