Yes, we did arm, Iraq, mainly so they could defeat Iran.
We also armed Osama so he could fight the Russians in Afghanistan.
Then they turned on us.
Had anyone ever taken the time time understand the arab mentality and thier creedo "the enemy of my enemy is my friend". perhaps we never would have gotten involved in thier wars.
Any arab/islamic nation will pretend to be our ally if we agree to help them fight thier enemy. Then at the end of that war, when we expect them to still be "our friend", they act like the 5 year old who says "I had my fingers crossed so I never was your friend".
This is one of the teachings of the koran - to lie, cheat and steal to get what you need to serve your cause.