Why do forces between the components of a chosen system never appear in the net external force?

1. Forces between components of a system come in equal and opposite pairs. 2. Both members of such a pair act on the same system, so they cancel. 3. Internal forces therefore contribute nothing to the net external force. 4. That is why the force between a lecturer and her cart drops out when both are inside the system. 5. Their size is irrelevant, since cancellation is exact whatever the magnitude. _Source: OpenStax College Physics (CC BY 4.0), Ch 4 "Dynamics: Force and Newton's Laws of Motion", section 4.4 Newton's Third Law of Motion: Symmetry in Forces_