Despite popular opinion the civil war primarily related to slavery, I understand Lincoln's primary concern was preservation of the union. Why did he care so much? What did he find so abhorrent about the southern states forming their own country?
It would set a dangerous precedent. If the southern states could secede, then potentially any state could do the same thing in the future if it didn't get its way. Democracy, at its core, is the rule of the majority. However if a minority could threaten to leave the union, then it wouldn't work. The United States would essentially become a failure - either it would completely dissolve, or become something very different from what the Founders envisioned.
Lincoln partially hints at this during his famous Gettysburg Address. He says, "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." So he was definitely concerned about the survival of the United States in a more general sense than simply worrying about the South breaking away.