There are many reasons why Lincoln and the north viewed secession as something that could not be allowed to happen.

1. It was important to maintain the US as a symbol for a functioning democracy. After the French revolution and the rise of Napoleon, people in favor of monarchies and whatnot seemed to fill vindicated in the failure of democracy. Lincoln understood his place in history and the importance of maintaing a mostly peaceful(besides the war) democracy as an example to the world.

2. The practically of the physical landmass of America. He said in his innaugral:

"Physically speaking, we cannot separate. We cannot remove our respective sections from each other nor build an impassable wall between them. A husband and wife may be divorced and go out of the presence and beyond the reach of each other; but the different parts of our country cannot do this."

Basically, the United States couldn't just break apart as they would be so close to one another and this would be a constant security threat. Slaves would continue to escape to the north and violent perusers might come with them. The south might try to align with foreign powers.

3.Lincoln also maintained that the very act of seccession was illegal. Again from his innaugral:

"I hold that, in contemplation of universal law, and of the Constitution, the union of these States is perpetual....It follows....that no State, upon its own mere motion, can lawfully get out of the Union; that resolves and ordinances to that effect are legally void; and that acts of violence, within any State or States, against the authority of the United States, are insurrectionary or revolutionary, according to circumstances. I, therefore, consider that, in view of the Constitution and the laws, the Union is unbroken."

A country in which the member states can leave whenever they want is a system that can't be maintained. It would allow a state to coerce the federal government into doing whatever it wanted because it could just threaten to leave. It would also give certain states undo power because a bigger, more important state, could just threaten to leave if they weren't given a certain power.

Though Lincoln did say things along the line of that he would maintain slavery if it meant preserving the Union, I do think Lincoln's actions against the south speak to an extreme dislike of slavery and he was rather horrified by it. In a letter from 1959 he wrote,

"This is a world of compensations; and he who would be no slave, must consent to have no slave. Those who deny freedom to others, deserve it not for themselves; and, under a just God, can not long retain it."

Even in 1855 he wrote,

"On the question of liberty, as a principle, we are not what we have been. When we were the political slaves of King George, and wanted to be free, we called the maxim that "all men are created equal" a self evident truth; but now when we have grown fat, and have lost all dread of being slaves ourselves, we have become so greedy to be masters that we call the same maxim "a self evident lie."

So to answer your question, it was a mixture of practicality, legality, and morality that led the North to move against secession.