This rests on the assumption that a democratic vote is sufficiently legitimate to alter the lives of millions against their will. If you base the decision to secede on a democratic election where the separatists win with 51% of the votes, you have 49% of voters--as well as their non-voting allies and kin--extremely displeased. If they win with 61% of the votes, you will nevertheless have 39% extremely displeased voters. You might associate separatists more strongly with the use of political violence, and think therefore that encouraging regions to put these questions to a vote might discourage violence, but what's to say separatists will not use violence to bring about that vote or to bring about their desirable outcome? Or, for that matter, declare a lost referendum invalid?

In addition to the practical concerns, there are the ethical concerns of letting one part of a country vote to damage the entire country and most of its citizens. Most countries have evolved organically over a long time in which important policy decisions have been made, based on the reasonable assumption of perpetual territorial integrity, with quid-pro-quo mutual beneficial arrangements. Allowing regions to secede based on referendums encourages them to take advantage of these relationships in an ethically dubious fashion.