One of the criticisms of Obama’s Afghan plan is that he announced a target withdrawal date. To his critics, that commitment to withdrawal (although it seems like a loose commitment) gives the Taliban strength by telling them they only need to wait it out for a couple of years. John McCain said “The way you win wars is to break the will of the enemy, not announce when you are leaving.” I don’t want to completely reject this view, because the tribes in Afghanistan have historically taken the long view, and 2 years is not long. But on the other hand, it’s not as if staying longer will necessarily help.
McCain views this as a traditional war, which it’s not. Al Qaeda and the extreme Taliban are religious nutjobs; we will never break their will, no matter what we do. But we can turn the moderate Taliban, and we can give the Taliban limited room to operate, by getting the average Afghan (Gul the Plumber?) on our side. And the best way to get them on our side? Give them security and then get the hell out of their country. Get their government to step up and provide services. A surge with a limit is a good way to do those things. It provides some security, it tells the Afghan government that it needs to get its act together, and it tells a people who hate occupiers that we don’t plan to occupy them. The marginalization of the Taliban that should come from all this will, I think, outweigh any psychic benefit that the hard core Taliban will get from an announced withdrawal.
Thoughtbasket 
Though I was originally opposed to more troops, Obama’s speech with specifics (like withdrawal) convinced me. As I heard somewhere today, Al Qaeda is a movement, not an army. So our “weapons”, as you say, need to be services, security and help with establishing a working government. In that way poor village boys have a future outside the fanaticism of the Taliban.
We should wage war to punish those who hurt us and protect our country (loosely borrowing from Mo Tzu). We should fight our wars in a way that achieve these ends. That did not happen during the term of the last POTUS who wanted to create two Utopian states along the Silk Road — talk about losing sight of objectives. If Obama manages to do serious damage to religious whackjobs who want to kill us, meaning enough damage that they will not try this again anytime soon, then he is doing the right thing.
You point out rightly that these are religious nutjobs. They slammed airplanes into buildings to please their God. This has never been a conventional war, but it can be a winnable one if we stay focused (get focused) on making terrorism on our soil too dangerous an option for these devout crazies.
But Zeus, what do we do about the right-wing Christian terrorists like Timothy McVeigh and the teabaggers calling for our President’s death? How do we protect our country from these devout crazies? The only difference between Oklahoma City and the World Trade Towers is the number of dead.