The president's failure to appreciate democracy-qua-democracy is legendary; taking his cue from right-wing sock puppet Hugh Hewitt (whose If It's Not Close, They Can't Cheat: Crushing the Democrats in Every Election and Why Your Life Depends on It came out after the 2000 elections), he seems to think that democracy is a sort of public spectacle, an excuse for potato salad and bunting, by which the public is allowed to vote in favor of the correct party. For him, elections are not unlike his service in the Air National Guard: a display, a perfunctory gesture through which one endorses allegience to the proper patriotic values -- but not anything to be taken particularly seriously, and certainly not anything in which an unexpected outcome (say, the fighting of an actual battle, or the election of an ideologically unsuitable candidate) should be allowed. His confounded, resentful reactions to open election results in Europe, Asia, and South America over the last six years tell you all you need to know about the esteem in which he holds the value of democracy; it's a principle worth going to war for, and worth wasting the lives of thousands, but it's not something you want to let decide who will lead a country.
Anyway, just in case the president wants to appear, in the future, slightly more informed about these matters, the reason that Hamas (and Fatah, for that matter) have armed wings is that, since Palestine is not a sovereign nation, it does not have its own military forces. Their armed wings function as combined police and security forces because, as an occupied territory of another nation, they are forcibly denied the opportunity to maintain a standing military. The only reason one does not say that the Republican Party in the United States doesn't have an armed wing is that, controlling the federal government as they currently do, they don't need one. Despite the best efforts of G.O.P. scandalmongers to make an issue out of Hamas' intention to use their own 'armed wing' as a security force, this is in no way different than what Fatah has done for the last fifteen to twenty years.
At any rate, we can all rest soundly at night, knowing as we do that if the President can't convince people that the Mahometan is a dire enough threat, American neoconservatives and lobbyists and the Israeli government can -- even if they have to commit treason to do it.