Lincoln always had two reasons in mind for fighting the civil war. One was opposition to slavery. The other was preservation of the Union.

He saw the secession as a threat to democracy.

"Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure."

Source: http://www.abrahamlincolnonline.org/lincoln/speeches/gettysburg.htm

In this great speech, that genius Abraham Lincoln managed to cover, in a few short words, both reasons for fighting the civil war: A democratic nation, 'conceived in liberty" cannot 'long endure' if the minority which is outvoted by the majority can just say, "Well, we didn't like that vote. We secede."

Democracy only works if a majority on a constitutional issue is binding. If it is not, democracy will not 'long endure' and anarchy, or some other form of government will replace it. So, "government of the people, by the people, for the people," would "perish from the earth."

The United States was "dedicated to the proposition that all men are created equal". Slavery is a denial of that proposition. Lincoln ran on a platform to ban the further spread of slavery into the territories. He didn't think (if elected) that he had the constitutional authority to ban slavery in states where it already existed, but he clearly thought it was incompatible with the essential tenets of the 'New Nation'.

It was, of course his election, bringing with it the promise of banning the spread of slavery, which caused the secession, threatening the concept of Democratic government.

Lincoln, quite eloquently expressed that the Union was fighting for two reasons, to oppose slavery where possible, and to preserve Constitutional Democracy as a form of government.

The war made the abolition of slavery possible (constitutionally) in the rebellious states (at least according to Lincoln's interpretation) and he took the opportunity and acted with the Emancipation declaration.

Victory in the war enforced the conclusion that secession due to opposition to a Constitutional majority vote was not allowable, thus preserving (in Lincoln's opinion) constitutional democracy as a form of government.