In Terminator Genisys, Kyle Reese goes back in time and we find out that Kyle is Sarah Connor's "mate" and John Connor's father even though Kyle was born 30 or 40 years after Sarah Connor.
A similar trip by Kyle to the past caused the birth of John Connor in an earlier movie. So there is a paradox. Kyle Reese goes back in time to protect the mother of John Connor but in that very same act Kyle himself becomes the father of John Connor. So that John Connor would not even exist in the first place if this recursive loop in time were not repeating.
So how did this loop begin?