So with less than 5 % of US oil coming from Iraq, how can it be argued that oil is the reason behind our invasion?

Well Iraq oil is a bit deferent from oil almost anywhere else in the world.  Chemically it is a higher quality than other countries oil. Then there is the location. Where many wells across the earth need to be dug deep, Iraq oil is relatively close to the surface so less digging. What that means is that where other countries pay ten dollars or more per barrel produced Iraq oil only cost 5 dollars a barrel. Lastly there is the amount of oil.

Iraq has a known reserve of 100 billion barrels. Much of Iraq is unexplored and estimates of further fields yielding anything from another hundred billion barrels to upwards of 400 billion more barrels.  

With very little effort Iraq could go from the second biggest reservoir on earth to the biggest by far.

So with the biggest reserves on earth, and lowest cost to produce, what country do you think now controls the flow of oil?

YA Baby.