A really good question.
The failure to compromise is of course an answer and one that was offered by a well-known American historian and author, Shelby Foote. But I believe the answer is because of the law. In fact, legal issues, split into two parts would be the answer.
First, slavery. Allowed since the United States of America was created, slavery was practiced in the Southern states and some border states (such as Missouri) where African Americans known as blacks and worse names were not considered citizens. They could not vote or own property either. This legal status had been affirmed by the US Supreme Court in the famous Dred Scott decision. Though not considered a reason for the war at first, it later became a reason and for Abolitionists and blacks the cause for what President Lincoln said "a new birth of freedom".
Second, state rights. Basically, what was more important: the laws and rules passed by Congress and the President in Washington D.C. or those in the individual states such as Ohio and Alabama? And if a state disapproved of a law did it have to follow it? This legal issue was a big problem throughout the 1850s as new parts (regions or sections) wanted to join the Union as states. It was a reason for the South seceding from the United States in 1861.
Finally, you may find this interesting but shortly before the outbreak of war there was an attempt at talking in the form of a compromise known as the Crittenden Compromise and shortly after the South declared its independence was the Corwin Amendment. Both failed.
The two legal issues I spoke of were solved with the 13th, 14th, and 15th Amendments.
Hope this helps.
Fairly powerful question posed. It truly is. I think that one of the lasting legacies of the Civil War is that if individuals truly hold and cling to their convictions in a liberal democracy, conflict is inevitable. One of the most compelling elements featured in the democracy in America, and perhaps all democracies, is the idea that compromise is a part of the package. Personal beliefs can be negotiated to avoid extreme hostility and ensure a level of common ground being reached. Yet, if one cleaves to their convictions and is unwilling to negotiate at their fundamental core, then conflict is almost guaranteed. Both sides, at their essence, believed in the authenticity of their convictions. The South felt that the issue of slavery was one of personalized notion of tradition and that the idea of freedom involved being left alone at the perceived intrusion of the North. For their part, the North believed that there should be nothing to stand in the way of the cohesive nature of the Union, and, in some parts, that slavery was a moral evil. Both sides could not resolve their difficulties through dialogue because these fundamental convictions lay at the core of each side's consciousness and could not be negotiated away. The Civil War proves, to a great extent, the potential for destruction within convictions in a liberal democracy.
The problem was that they had tried talking it out already and they had gotten to the point where they had nothing left to say.
The North and South had been arguing over the issue of slavery ever since the writing of the Constitution. The Constitution had a couple of compromises on that issue written into it.
Then the two regions had to argue about and compromise on the land from the Louisiana Territory (Missouri Compromise). They talked about tariffs and had a huge argument about that in the late 1820s (Tariff of Abominations). They talked about their problems during the Mexican-American War and they talked about them some more after we won that war (1850 Compromise).
But after such a long time, it got to the point where neither side could persuade the other and their interests were in so much conflict that they had to fight. They had talked and talked and never solved the issues so they stopped talking and had a war.