In this theory, Skynet, having been aware of John's successful mission to destroy it in the future, might have become confused or desperate to preserve its existence. When John is infected and sent back in time to become a part of Skynet, a paradoxical situation arises. If Skynet succeeds in killing Sarah Connor, it would effectively erase its own existence since John, the very piece of Skynet responsible for its survival, would never be born.

This presents an interesting twist in the narrative. The Terminator sent to protect Sarah Connor might not be there to save humanity but to ensure the survival of Skynet itself. By protecting Sarah Connor, it aims to preserve the events leading up to John's birth, ensuring that he becomes infected by Skynet and eventually sent back in time.

In this scenario, the Terminator sent to protect Sarah Connor becomes an agent working indirectly for Skynet, attempting to ensure its own survival by maintaining the timeline that allows John Connor to exist as a part of Skynet.