The political theorist and idealist in me says, the states should absolutely have the right to secede. Self determination is considered a basic fundemental right by most people in the West. Our own nation is based on the concept that the consent of the governed in crucial to the legitimacy of any government.
However, the realist in me recognizes that those rights are only applied by groups with suffcient military power to defend those rights from the government they seek to secede from or have allies/benefactors who will use their military might to defend that right. Allowing the South to secede, while it may have satisfied some theoretical purist view on the right of self determination, would've been disasterous for this country. The Federal government, which is charged with looking after the best interests of the nation, was correct to refuse to allow secession and put an end to it by force of arms.