Once the communist government fell, a coalition government formed of the various mujahedin factions was formed. This quickly degenerated into a free-for-all of what little resources Afghanistan had.
The rise of the Taliban was due in no small part to the disgust Afghan traders had with the warlords and the lawless environment they created.
Resistance was limited and fractured, while the Taliban remained a cohesive whole. By the time the warlords united under Masood, the Taliban controlled most of Afghanistan.
The US never trained the Taliban directly, since they emerged as a real force only after the withdrawal of Soviet forces. Some of the mujahedin we trained and armed during the war did join the Taliban (and more so as the warlords were defeated), but we never proffered direct aid the Taliban as an organization.
I also don't believe the Taliban are anti-American, per se. They are attempting to create a closed, fundamentalist state, and consider American culture a deadly influence to the society they want to keep. Their fundamentalism is more of an internal nature than an external nature, although surrounding nations are naturally concerned that the Taliban will try to spread their Islamic revolution. They are bitter about American support of the opposition and the sanctions on the Taliban, but they have also shown signs that they are will to work with the US when necessary, and won't require deviating from their strict religous beliefs. For example, the Taliban drastically cracked down on the opium trade when Iran and America requested it (and monies received from the US didn't make up for the profits derived from the opium trade).
So why do they harbor bin Laden? bin Laden supported the mujahedin during the Soviet occupation, and was one of the early supporters of the Taliban when they began their jihad. They owe him a lot, and if that means facing off against the most powerful nation in the world, so be it. It's not that they hate the US (well, they do, but not enough to do anything about it), it's just that they owe bin Laden more than they owe the US.
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