The Terminator series is a paradox. In the future, Skynet sends a Terminator (T-800) back to 1984 to kill Sarah Connor, John Connor's mother, to prevent John's birth and the subsequent resistance against Skynet. The resistance sends Kyle Reese back in time to protect Sarah Connor. Kyle Reese and Sarah Connor conceive John Connor in the process. This means John Connor exists because of the events triggered by Skynet's attempt to stop him, creating a paradox that cannot be escaped.
Also, Skynet exists in the future because the T-800's arm and chip are in possesion of cyberdine systems, which they reverse engineer to create Skynet by using the same tech skynet sent back in time. This creates a bootstrap paradox where Skynet's creation relies on technology that only exists because of Skynet's actions in the future.