America didn't train the Taliban, that was the ISI. AQ had backing from many people in the Arab world, and their tactics weren't taught by them AQ hooked up with multiple other terror networks to actually build their doctrine, AQ was associated with the Chechens who had used AQ's tactics aside from flying planes into buildings against Russia during the 90's.

Pakistan though supported both AQ and the Taliban, the TTP (Pakistani taliban) was only founded in 2007 as a result of the US, and Pakistan cracking down on AQ in Pakistan.