Like arming the Nazi SS to defeat Hitler

Opinion
Why did we go to war after 9/11?
I had understood that it was to get Benny and to defeat Islamic terrorism.
You know the sort of people who kill and rape people in the name of Allah?
So, why did we help put in power one of the must extreme Islamic terrorist groups, in Libya Egypt, Syria and soon Jordan, Pakistan and  Iraq, and arm al-Qaeda to do it?? 
That is rather like giving arms to the Nazi SS to defeat Hitler.
Have we gone out of our minds???????