A Newton's third law confusion Suppose you have a bird inside of a glass cage with some amount of gas inside it.
We now place this cage on a weighing scale and observe its readings in different situations.
Case (1): when the bird is resting with its feet on the cage, the weighing scale measures the weight of the bird and the cage.
Case (2): when the bird is hovering over the cage (its feet is not in contact with the cage and it is at the same position), the weighing scale still gives the same reading.
Explanation: the bird pushes air down at a constant rate in order to stay hovering. This air collides with the bottom of the cage with a force that makes up for the weight of the bird (Newton's third law).
Now this is the confusion:
Case (3): when the bird is accelerating upwards with a particular acceleration.
Viewpoint (1): the bird, the cage and the gas form the system. The acceleration of the bird is an internal acceleration. Internal acceleration does not induce a net force on the system. Hence the weight measured by the weighing scale does not change. This is a consequence of Newton's third law.
Viewpoint (2): by Newton's third law, the acceleration of the bird is achieved by pushing air downwards with a force equal to the m(g+a).
This air collides with the bottom of the cage with that force, hence imparting this force to the bottom of the cage.
The weighing scale will now weigh more.
We have used the same Newton's third law, but have gotten different results. What is the error?
 A: Viewpoint (2) is correct. In order for an acceleration to count as internal acceleration, then the center of mass of a system cannot change its motion (this is also how one distinguishes internal from external forces). Since the bird is accelerating upwards, the center of mass of the bird + cage is accelerating upwards, which means there must be an external force present--namely, the extra force of the scale on the bottom of the cage to counteract the increased force of the air pushed down by the bird.
If the bird cage were on the International Space Station in orbit around Earth, then the cage would be accelerated downwards as the bird accelerated upwards.
A: 
Internal acceleration does not induce a net force on the system

This net force is force that can be thought of as applied on the center of mass. But you are not measuring this. You are measuring the force which cage exerts on your weighting scale. 
When bird accelerates upward, to keep center of mass still, the cage must accelerate downwards, thus producing bigger force on weighting scale. 
