It's hardly surprising that Serbia would reject as unlawful the declaration of independence by Kosovo. Countries with restive minority populations almost invariably resist separatist movements---and sometimes with good reason. For example, where the national majority (here Serbs) forms a substantial minority in the would-be breakaway nation, the larger nation may legitimately worry that independence will bring persecution of those of their group in the new country. The larger country may also worry that the very tensions that lead to an independence movement in the first place will continue post-independence, with a risk of war thereafter. More problematically but not irrationally, the would-be breakaway may have natural resources that the larger country does not wish to lose.
But sometimes resistance to independence may be irrational, simply a reflexive nationalism. Surely there are circumstances in which holding onto the would-be separatists is itself the source of much of the animosity. Certainly that is how many Russians feel about Chechnya, for example.
Conversely, the one true success story is the dissolution of Czechoslovakia into the Czech and Slovak Republics. As is frequently the case, so too here, the ethnic group that was less materially successful (the Slovaks) wanted out, and as so rarely occurs, the Czechs had the good sense to let them go. Both countries---but especially the Czech Republic---have done well since.
Where the country from which severance is sought is a non-democratic state, it's hard to see that any tears should be shed when the smaller unit leaves. But in a democracy, the desire of an ethnically-based majority of a geographic sub-unit to part ways can be experienced by the larger polity as a shock or even an insult. This, I think, may explain the Canadian dynamic. It is by no means clear that Canada would be worse off if Quebec (and perhaps the maritimes) were to become a separate nation. But Anglophone Canadians experience Quebec separatism (such as it is) as a challenge to their conception of Canada as multicultural country in which nationality is not ethnically based.
Posted by Mike Dorf