Then why not simply ask for a declaration of war?
I'll tell you why. Because since 1945, both Presidents and Congress have wanted to take the easy way out. Presidents want the complete freedom to act, and Congress doesn't want to take the responsibility to declare war.
If I'm wrong, please correct me. But please include in your response an answer to the above question: If you're going to go to war, why not simply ask for a declaration of war?
Yes, you’re wrong. First of all, in the case of Afghanistan, there was no nation-state to declare war on, but rather an organization (Taliban). One could argue that they were one and the same, but the Taliban wasn’t in complete control of Afghanistan, IIRC.
Secondly, you’re arguing syntax when the semantics are the same. If Congress authorized the commander in chief to deploy the military for an objective, it doesn’t matter if they use specific magic words or not. The granting of authority is the end result.