So what. If the definition says that 1 shot per pull of trigger and since the trigger is moving back and fourth for each shot how would this not fit the definition.

Because it doesn't fit the definition as it has been and is interpreted by BATF and the courts. You can contact the BATF and get an official read directly from them if you wish.

From past rulings the BATF says that the key is that the SHOOTER must be what operates the trigger once for each shot. If a spring or or some other mechanism is what operates the trigger then it's not going to be legal.

The shooter must do something each time the gun fires--he must physically operate some part of the firearm by manually moving it a noticeable amount for each time a shot is discharged.

If you can make a single movement and then remain motionless while the gun continues firing then it doesn't matter how the mechanism accomplishes that operation--doesn't matter if the trigger moves each time the gun fires or stays motionless against your finger. The firearm is a machinegun if it fires more than one shot without your having to do anything other than move once.