So I just watched Terminator: Genisys. Then I watched videos explaining all the timelines. The explanations were all well and good and fairly similar across the websites.
But this is what I don’t get. A Terminator is sent back in time to kill Sarah or John Connor. The only reason given in the movie and on the websites is that by killing either of them, John would not be able to lead the resistance against the machines.
While I can easily understand Skynet does not want John to lead the resistance, it doesn’t guarantee success. Yes, you stop John from leading the resistance, but that doesn’t mean someone else would not rise to the role of leader and stop Skynet. Given the power of time travel, it would seem to me there are better choices in guaranteeing Skynet's survival.
Why is Skynet utterly obsessed with killing John Connor?