Hi guys,
I almost forgot about this until you guys brought it up again.
Anyway, this is the answer I got from Airbus. There's a requirement for certification that the engines are not fed by the same fuel tank. A321 meet this requirement because center tank fuel is transferred to the wing tanks first, then from wing tanks, fuel is supplied to both engines. But for A320, center tank pumps will have to be off until take off is completed to meet the requirement.
I do not know how Boeing managed to "circumvent" this requirement but probably like LEM said, Airbus always think they planes are better than Boeing thus their requirement are more stringent.