[Ari]

I would be very curious to see evidence that shows the old Iraqi government was paying money to Al Qaeda bomber families.

Claiming that removing supposed terrorists in Iraq (which so far hasn't been completed) is making the world safer, is like saying that halving our original cold war nuclear weapons stockpile made the world safer. Or that standing next to a 5000 pound bomb is safer than standing next to a 20,000 pound bomb.
By committing our soldiers to hold iraq, it allows terrorists everywhere outside of iraq easier travel. In standard war, a common strategy is to force an army to commit troops to a specific area, to dwindle their supply in other areas. This was used to our advantage in WWII when the Nazis committed troops to Russia allowing an easier victory in europe.