Now, let me say a few things about this. My wife might still arguably be a dual citizen since I don't think she's formally renounced the citizenship of the country she was born in. Children are a different case. They should be allowed to wait until their majority to decide which citizenship to choose. And I recognize that that there are some transnational families where there are practical reasons why it may be convenient to hold two passports or impossible not to do.
My point in making these caveats is simply to point out that I don't have any personal beef with people who carry a US and Canadian passport or a US and Israeli passport and let's not forget Marcus Bachmann who has a Swiss passport.
But at least at the level of principle, citizenship is unitary -- you can't be a citizen of two countries any more than you can be married to two people at the same time. Some people find this nationalistic or xenophobic. But it's neither. To me it's at the root of our equality as Americans. That's why the Salvadoran immigrant to the woman whose ancestors came over on the Mayflower because they've both cast their lot as part of the same national community. If citizenship is purely transactional, the people who lack power are profoundly disadvantaged. (I wrote more about this several years ago.)
I bring this up because of the news that Eduardo Saverin has renounced his US citizenship, basically to escape the country's tax burden. This is admittedly a bit different than dual citizenship. But for me it's part of the same equation. I believe in robust citizenship. It matters to be an American. It's not just a passport. It's a national community, not something to be tossed aside or to be hedged. Again, in my mind it's a citizens greatest claim to equality, equal membership in a national community.