No. A war as vast and destructive and long lived as that one had many reasons and many animosities. Your statement has two parts. The defense of slavery would have no avail to the South since slavery was permitted by the Constitution and Lincoln had stated his approval of its continuation in order to preserve the union.
The issue of expansion does have teeth. There was a true contention in that issue. The states, at that time, were sovereign (unlike today thanks to Lincoln) and the South would have made the issue of slavery a sister issue with the other rights of newly formed states. "The government had violated its contract with the people."
But the southern leaders were committed to the free expansion of slavery into the territories, and saw any threat to that expansion as a threat to slavery itself. Lincoln was uncompromising in his opposition to the expansion of slavery in any way, shape, or form. He knew that if it was limited to the states where it currently existed then it would eventually die out on its own. The southern leadership would not tolerate what they saw as a threat to the institution itself, so that was their primary reason for the rebellion.
The states, at that time, were sovereign (unlike today thanks to Lincoln) and the South would have made the issue of slavery a sister issue with the other rights of newly formed states. "The government had violated its contract with the people."
But there you run into that same old tired southron line which is 'the states were sovereign' meant only what the southern states wanted it to mean. How can a state be sovereign if it was forbidden to ban slavery, which is what the southern leaders wanted? The southerners wanted the right to move with their slaves wherever they wanted, regardless of the wishes of the people in the states. So they wanted sovereignty when it was convenient to them, and an overpowering central govenment when they found that benificial. Kind of how the Davis regime turned out.