So let's think about this: Maybe the thing that makes John such a great leader is that it's in Sarah's blood. After all, we've seen that Sarah has badass inside of her in the first and especially second movies. So in the original timeline, Sarah gets knocked up by random 80s dude, Cyberdyne manages to create Skynet without any help from future technology, John Connor grows up and survives the nuclear holocaust, and ends up being an awesome leader and kicks the machine's ass until they decide to use their fancy time travel technology to go back and wipe him out. Only this time,