The Taliban was initially defeated and driven out of the country or into impotence by the force of American arms, but al Qaeda was not found. Sensing an undesirable lull in American post-9/11 jingoism, Dick Cheney and his Petroleum "committee" realized that American attention could be refocused on a more attainable goal, in Iraq, by the simple expedients of transferring significant culpability for the 9/11 attack to Saddam Hussein and to underscore his penchant for treachery and his evil nature by attributing to his regime weapons of mass destruction&mash;weapons like poison gas he used in the Iraq-Iran War, but also nuclear weapons, which he did not ever have. Americans caught on, and soon enough Afghanistan was relegated to the back seat and policy on the ground decayed into thoughtlessly annoying the civil population, thus providing aid and sustenance to the Taliban and to al Qaeda. The former reorganized and the latter found additional safe haven in troubled Pakistan, where it dawned on both al Qaeda and the Americans that Pakistani nuclear weapons (aimed primarily at hated India) were now possibly in play in the conflict over what Afghanistan would become.
Americans soon enough learned that Afghanistan is not really a nation in the modern sense. It is a small collection of modern urbanites and mostly deliberately non-modern tribes eking out a living from a territory ill-suited to anything resembling life in the west or the far east. It is a poor country with few prospects, except for opium production. So, add narcotics to the list of things that Americans wished to extirpate, but have not had much success in either.
As Americans consider what would be nice to accomplish versus what is reasonable given the amount of resources and number of lives we are willing to sacrifice to accomplish, each layer of intention, we find ourselves backed into yet other corners both domestic and abroad. NATO is shouldering a small part of the burden of finding al Qaeda and, willy nilly, of helping to establish some kind of civil order from among the various forms of tribal allegiance and political corruption that turn out to be Afghanistan's chief domestic product. NATO in the same book is not on the same page with America at the moment, because American really does not (or has not stated) its current objectives in Afghanistan.
It is clear enough that the military have the usual internal incentives to remain and fight out some kind of a mission, for that is what militaries do—fight. It is also clear that the military-industrial complex back at home stands to profit from a continuation or escalation of hostilities. It is also apparent that the domestic economy needs help and that stimulation through the m-i complex will do that, and more to the point, the reverse—cessation of hostilities—would have the opposite effect on the economy and prove to be the undoing of much else that the Obama administration needs to carry off successfully.
It is speculation that General Petraeus entertains political aspirations, but these rumors cannot be discounted, and so there exists another dimension to the problem, namely whether continuing the war will lead to a) failures which will detract from Petraeus's reputation, or b) will provide Petraeus with documented evidence of the insufficient hawkishness of Obama as Commander in Chief.
The mission "cake" in Afghanistan is many layers deep by now, and iced/frosted with political considerations that have very little to do with cake itself and more to do with the nattering of politicians in Washington. The Republicans, despite their own natural patriotic interests as citizens that Obama succeeds, are doing everything they can to frame the Afghanistan questions in terms of the alleged incompetence of Obama and Democrats in general to prosecute a war successfully or to maintain adequate national security. Democrats, generally taking more into account than the immediate political remuneration of any line of thought, have done a reasonably good job of sneaking the real issues into the news ... partly because the media are still smarting from its own complicity in the fraudulently promoted Iraq War.
Obama's private meeting with General McChrystal, whose voice for more troops is expectable, but not excusable in terms of chain of command, must surely have included a not-so-subtle reproof against the General for shooting off his mouth, but also a couple of attaboys to keep him in the belief that Afghanistan is really not the miserable mess that Cheney and his predecessors allowed it to become, and that there is a mission out there somewhere that Americans with NATO's assistance can prosecute successfully.
Frankly, I do not know what that mission might be, since the original goal of finding and routing al Qaeda seems less than likely to be accomplished and all else is predicated on that mission being the focal point. That being said, I think we can be assured that muddling the mission will be the best tactic until the mid-term elections of 2010 are over. If the Democrats lose the House or the Senate (but probably not both), then the mission in Afghanistan becomes anybody's guess, but muddling will not work again.