Unfortunately, I saw this discussed all over the interwebs before I had a chance to read the massive Action Comics #900, which (also, even primarily!) contained the final chapter to Paul Cornell and Pete Woods' marvelous "The Black Ring" storyline (featuring several guest artists), which they tied into the "Reign of Doomsday" crossover (with the help of Jesus Merino) that will continue in next issue of Action.
But as amazing and spectacular as Cornell and Woods' tale was (I can use those terms to describe a DC book, right?), all the media focus is on a 9-page story written by David S. Goyer (and beautifully illustrated by Miguel Sepulveda) in which Superman tells the president's national security adviser that he plans to renounce his U.S. citizenship in front of the U.N. (YouTube would seem a better place to do that--worked for Maxwell Lord in Justice League: Generation Lost #24, right?)
The widespread media interest in our world is understandable, of course, since Superman has long stood for "truth, justice, and the American way," and the decision is being interpreted as a commentary on current U.S. policy (as was the death of Captain America years ago, and more recently the "unpatriotic" changes to Wonder Woman, both in the comics and on TV). His ties to the United States have been downplayed greatly in the comics for decades, where he is normally portrayed as a "citizen" and protector of Earth. But in the popular imagination, not the minds of the comics-obsessed, Superman is closely associated with the United States, so this action caused an uproar.
In the story, Supes seems to have (at least) three possible motivations behind this decision, ranging from the more politicial to more philosophical. He makes the political motivation explicit to the NSA: "I'm tired of having my actions construed as instruments of U.S. policy." I think this is very reasonable and prudent, and actually (and ironically) protects the U.S. more than it does Superman. It frees him to intervene in situations around the world, including nations and regions where American intervention is less than welcome--such as the motivating incident in the story--without implicating the U.S. government (which, after all, is what the president in the story--DCPOTUS, if you will--is concerned about).
Second, as protector of the Earth as a whole, his adoptive world and home of humanity, he doesn't want to be seen as advancing American interests in particular. He hints at this when he says "'Truth, justice, and the American way'--it's not enough anymore. The world's too small. Too connected. ... I'm an alien... I can't help but see the bigger picture." As strange as it may be for Supes to say these words outloud, I think most people understand this is how he thinks. After all, even Captain America has defied the U.S. government when he disagreed with specific policy positions; even he will not act solely in U.S. interests when there is a greater principle at stake. I don't think anyone doubted Supes would either, but maybe I'm wrong.
Finally, and this is the most speculative of the three motivations, Superman may be renouncing the ideals that American stands for (even if its service to them is not always perfect), such as liberty, equality, and democracy. He may be implying as much when he casts doubt on "the American way" (my emphasis) and his invocation of "the big picture." But certainly his actions in the "incident" reflect those ideals, and more generally one has to wonder: if not those ideals, than what? Again, look to Captain America, who has long been able to distinguish between American ideals throughout history and American policy at any point in time; he has disagreed with the latter while never wavering from the former.
I really doubt Superman is abandoning the ideals of liberty, equality, and democracy--after all, these are hardly uniquely American values--and I interpret his renuncation of U.S. citizenship as a practical, political measure meant to insulate his actions from U.S. policy, freeing up both him and the U.S. to pursue their own goals and interests.
Was the way it was written a bit inelegant? Probably. Did it shock? Of course. (Was that the goal? Perhaps.) But I think it can be reasonably be understood just as Supes explained it--a eminently prudent measure, which was blown out of proportion (in the real world as well as in the story--very prescient, Mr. Goyer!). We can only wish that political decisions in the real world could be made so well!