The problem with self-determination is that it is implicit anarchy. No, it's not necessarily doing away with government (rather, it is creating a new one), but philosophically, it is aligned with anarchy. Once you allow self-determination as a principle, by that same principle you have to allow anyone to be self-determinate. It may sound far-fetched, but, in other words, I should be able to be my own country.
I think asking questions about the legitimacy of self-determination is a de facto encounter with anarchism. Can you accept anarchy?
And, to clarify, by anarchy, I don't necessarily mean a complete lack of government (although it can be); I mean that self-determination opens itself up to a multitude of non-hierarchical systems or "systems" of governance.