After the Soviets withdrew from Afghanistan in 1989, the US had no incentive to be involved there anymore (remember we used this war as a proxy war against the USSR). So we turned our influence/power in the region over to the Pakistani intelligence agency (the ISI), and left the Mujahideen groups to split and war between themselves.

The ISI found this power vacuum rather… convenient. They became buddies with the Taliban and its warlords (for trade route purposes), and helped them during the Afghan Civil War. With the aid of the ISI (and financial aid from Saudi Arabia), the Taliban took over most of the country by 1996.

The new Taliban regime initially rejected bin Laden’s al-Qaeda (after both Sudan and Saudi Arabia had banished them), but eventually warmed up to the thought of being their friend. When they inevitably became allies, the Taliban allowed al-Qaeda to have shelter within their borders, and integrated the terroristic organization into their military. 

At this point, the Taliban assigned al-Qaeda to train 055 Brigade, which was a strong part of the Taliban’s military (made up mostly of Soviet-Afghan war geurilla veterans). This brigade was in fact used for al-Qaeda’s terrorist activities (such as the 1998 bombing of the U.S. embassy).

Needless to say, they were really good friends. Al-Qaeda was practically a dependent arm of the Taliban regime. Pakistan only ever set up this alliance, albeit they remained friendly with both organizations from the 1980’s. But Pakistan only supported al-Qaeda after the 2001-present phase of the War in Afghanistan commenced.

Invading the Taliban was the correct choice, not Pakistan (as good-gollymissmolly would suggest). 

Though to be fair, the entire conflict was initially our fault in a multitude of ways:

• 1) The Cold War was an avoidable conflict, easily remediable by swift action immediately following World War II. 
• 2) We (our CIA) funded and supplied the Afghans in the Soviet-Afghan war through the ISI, thus creating weakened regimes, allowing for the power vacuum that inevitably assisted the Taliban just so we could say “HA!” to the Soviets.
• 3) The Taliban and al-Qaeda were/are also mainly composed of soldiers that we helped; Osama bin Laden was among these soldiers (under the alias of Tim Osman).
• 4) We continually involved ourselves elsewhere in the Middle-East (like in Kuwait or in the Iraq-Iran affair), escalating situations that in turn entangled the regimes all over the Arabian Peninsula, disturbing alliances/conflicts further.

Still, overthrowing the Taliban was necessary after they refused to hand over al-Qaeda following the September 11 attacks (even though the conflicts that 9/11 was contingent upon were our fault). Attacks on our soil should never go unchecked.