Well, most histories say he did. He did not want to be perceived as weak after 9-11.
The CIA and military raced to see who could come up with a plan to attack the Taliban first. At every meeting W would pressure folks for their plans. The CIA had some contact with the Northern Alliance, a group of fundamental Muslim tribesmen who did not like the Taliban and were the first to go into action.
The problem is, and was, that there was no definition of "winning" and no exit strategy. As the Russians learned in Afghanistan and the Muslims are teaching the Americans in the same place, it's probably wise to have a goal and exit strategy. At first it was the removal of the Taliban and the demise of OBL. Those have been accomplished and we're still there.