I am going to do a little conjecturing here. This just an idea I have had over the years and it is based on knowing something about how the players involved think but with no actual knowledge if such a discussion ever took place. I am going to take some liberties in my descriptions for the sake of brevity and style.
I can imagine...
Bush, Cheney, Rumsfeld and Rice sitting down after 9/11 and after they have an idea that it was an Al-Qaeda mission.
Cheney is the strategist, Rumsfeld is the logistician and implementer and plays the devil's advocate role, Rice provides historical context and a read on the global picture. Bush is the decider, now directly faced with the problem of making sure the U.S. is safe. They all are serious and they have enough respect for each other that they can throw out ideas without fear.
They already know they are going to hit Afghanistan hard and take out the Taliban who hosted Al-Qaeda and Osama bin Laden. They don't know if they will be effective in hitting Al-Qaeda itself cause the intelligence on the organization is sketchy at that point and they have just started ramping up the massive intelligence operation which will give them actionable data.
They are also just starting to recognize that the wall between the nation's law enforcement and intelligence assets was a part of the major failure to stop the attackers before they acted (we are returning to this mindset right now with the Obama administration, another lesson wasted and another lesson that is destined to be learned again the hard way.)
After discussing military and intelligence options for Afghanistan the discussion get elevated up a notch and two questions are posed -
1. Where is the greatest existential threat to the United States coming from?
2. What are we going to do about it?
The topic is thrown around and Cheney, Rumsfeld and Rice come up with the same answer - the crescent of the Middle East and Southwest Asia.
This area is generally hostile to the US and the West, controls most of the world's oil, is rife with unstable or totalitarian governments, hosts a virulent, violent and expansionist form of Islam, has the infrastructure potential to develop nuclear and other forms of WMD.
A map is brought out and the area is dissected at length.
Strategically, Israel dominates its neighbors. Though small in population and land mass it is capable of significant force projection should it need to. They are the only democracy on the map. They are seen as an ally economically and culturally, but they are not a client state and thus somewhat of a wild card.
Syria is Ba'ath and tied in with Iraq, though uncomfortably. They are pre-occupied with Lebanon and Israel.
Lebanon is a recurring mess, but it is mostly the Israelis that need to worry.
Jordan is not a democracy, but they are friendly when they are not pre-occupied with the Palestinian diaspora.
Egypt is focused on internal affairs and has stepped back from influencing the course of events in the region.
Turkey is moving toward the EU and provides an anchor in the region.
The Gulf States are tied into the West economically, but are vulnerable to internal disruption if Wahhabism spins out of control and external threats in the case of attacks by Iraq or Iran. The stability of the West is dependent on the flow of oil from these states.
Nuclear Pakistan is focused on India and is struggling to catch up with its much more powerful neighbor. The areas abutting Afghanistan are no man's land, but the Pakistanis don't much care.
Afghanistan is going to be invaded, no question about that, but the Taliban government is primitive, a throwback to medieval times and has no force projection outside its territory.
Iran is a very large country with a large youthful population. It is dominated by a theocratic elite which is not always fully aware of what drives people of other faiths and non-theocratic governments. They are still excited by the revolution they went through and junior leadership is just starting to move into senior positions. They can only do so by showing a commitment to exporting their revolution. They are the most significant destabilizing force in the region and provide funding, training and a base of operations for direct action teams that target Israel and the West.
The group looks at the map again and smack dab in the middle of it is Iraq.
A large country with significant oil and gas resources it continues to be a bad boy in the region. It is believed to host terrorist training sites and it continues to financially support Palestinian suicide bombers. It is led by a sociopath that has a long history of attempted expansionism and cruel domestic suppression. It is under UN sanctions for failing to respond to nuclear inspections and there is a growing concern that there is a well hidden development activity to produce nuclear munitions.
The most important thing they notice is the geography - Iraq is bounded by Turkey, Syria, Jordan, Saudi Arabia, Kuwait and Iran. It is in a position to influence the entire region and often does so to the detriment of American and regional interests.
The group pauses and considers a strategic approach to long term stabilization of the region they consider the most likely to affect the US and the West.
They could hit Iran, the largest exporter of terrorism, directly but it would be a costly campaign, getting an allied force together would be close to impossible and the outcome of a long term occupation would be in doubt.
Iraq, by process of elimination is thus the natural choice for a projection of power. Oil is not a factor, stabilization and the imposition of a democratic government that can act a model for the rest of the region is.
Iraq is now evaluated as key to a Mid-East containment strategy.
If Iraq can be made to go democratic or become a client state it will directly influence the populations of all of the countries of the region. It would be a classic implementation of one of the ancient principles of strategy and war - establish an invulnerable base in the midst of your enemy and then selectively seek to influence them to your side, or destroy them.
The die is cast, the rest is history.
Authorization For Use Of Military Force in Response to the 9/11 Attacks (P.L. 107-40): Legislative History