You generally believe in the concept of democracy, right? Then if the people of a given area decide to secede peacefully via referendum, then the burden of proof is on YOU to prove why they can't exercise their democratic right in this way.
The burden of proof sure as hell is not the way you say it is. Democracy does not equal having a majority gets whatever the heck you want. It is rule of laws, both written and unwritten.
A secession, even one endorsed by a majority of the seceding area, would be a flagrant violation of many agreements and obligations entered into in good faith. For starters the substantial unionist minority would be grossly infringed upon, being deprived the right to maintain their citizenship in the status quo, the most fundamental right we have. It's not incumbent on us to say why the majority can't do whatever they want, it's incumbent on you to say why the minority should be made to suffer so greatly. Add onto that the massive breach of faith with the rest of the country which has faithfully honored the rights of the area that now wants out.
There would be nothing democratic about such an action. Democracy empowers the citizens, not makes them victims to extralegal processes that overturn the civil order on the flimsiest of grounds. If you want a democratic secession then it needs to be built on democratic grounds. Show systematic disenfranchisement. Show there is not fair recourse through the existing channels. Show that the breach of good faith lies not with those seceding. If you can not show these things then what you are proposing is not democracy, it's a power grab.
The classical liberals who you libertarians claim to love all wrote about how you don't go rewriting the social contract on a whim. Even the downright anarchistic Rousseau, who said that people have the right to leave the state, said that they can not desert their obligations when you do so. A liberal society is not a society where laws don't constrain our actions. It's a society where bad laws don't constrain our actions. So if you claim you should be able to ignore the law without first showing that the law is unjust then you are rejecting the fundamental principles of democratic government.
tl;rd Read any political philosophy from the past 400 years and get back to us, thx.