Part of the reason why I'm willing to consider and in some cases support the idea of secession (e.g. - here and here) is that I take a very instrumental view of government. I believe that existing governments, if they have any merit at all, are valuable only as means to other ends. To greatly oversimplify, I think that government is valuable only in so far as it promotes the the values of "life, liberty, and the pursuit of happiness" that were the main justifications for the establishment of the United States. If I am persuaded that some major alteration of current political arrangements would achieve these objectives more fully or at less cost, then I'm perfectly willing to embrace it. I don't see the U.S. government - or any government - as having any intrinsic value. If a particular secession seems likely to increase freedom and happiness without causing harm that outweighs these benefits, I'm willing to support it. In this respect, I am similar to most other libertarians, and also to some (but by no means all) political liberals, who also often view government in purely instrumental terms.
Many people - nationalists, many conservatives, and others - see things differently. They believe, at least to some degree, that states have value in and of themselves, apart from the instrumental purposes they serve. People who think this way often view secession proposals not only as wrongheaded, but as morally anathema. To them, advocacy of secession is not just misguided, but also immoral.
Ironically, my instrumental approach to secession and the value of states also puts me at odds with some secessionists. Specifically, I differ with those who justify secession on the grounds that their subnational political regime has intrinsic value of its own that justifies giving it the trappings of full sovereignty and endowing its government with a moral "right" to secede, regardless of its reasons for doing so. Sometimes, such claims of intrinsic value are based on ethnic nationalism (as in the case of Quebec secessionists); other times on legalistic grounds (as in the case of the American Confederates).
Obviously, I can't even begin to fully resolve the conflict between the instrumental and intrinsicist views in this post, which is intended merely to highlight the key difference between them. I would note, however, that the American political tradition was initially founded on a strong version of the instrumentalist view . By 18th century standards, British rule over the American colonies was relatively benign, and the American rebels could not claim that their colonies deserved independence because they were ethnically distinctive or had intrinsic rights of sovereignty (after all, their power was initially granted by the very British government that they sought to secede from). Instead, the Declaration of Independence articulated a strongly instrumentalist view of government, and justified secession on the grounds that British rule was beginning to undermine the instrumental purposes that it was supposed to advance:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government.... . [emphasis added]
To say that an intrinsicist view of the value of government is inconsistent with the Declaration of Independence is not to say that it's wrong. Perhaps it was the Founding Fathers who were in error. Personally, however, I think they got this particular point right.