I tried to analyze the whole John Connor birth a few time.
Kyle goes back in time and fathers John.
>>
John sends Kyle back in time.
>>
Kyle goes back in time and fathers John.
ext ext
What's going on is a loop, but not definitely an infinite loop.
If Terminator is to be looked at realistically - John Connor's original father must have been someone else. Someone from Sarah's time. Perhaps someone who didn't stick around to ever meet him, maybe even a relative of Kyle. Either way,the original John Connor, with his original father, and without any warning or preparation, had the capability to save the world from the Terminators.
For all we know, that was the first John Connor or John Connor 1 he sent back the original Kyle.
Now from the first movie, the father of that John Connor is Kyle. He had preparation. that is at least John Connor 2. you could make the argument it's John Connor 2+, meaning all John Connors after time travel are identical, but that cannot be true.
You can also make the argument that John Connor 2 was never attacked by the T1000 unit. Instead that John Connor grew up, and like John Connor 1, despite having a different father and different upbringing because of Terminator 1's events, won the war on the machines, which led to them sending back the T1000, sparking Terminator 2 - and creating John Connor 3.
Now John Connor 3 is slightly different than John Connor 2, in that as a young teen, he met a 101 unit and was attacked by a 1000. His foster parents were murdered and his mom got out of the insane asylum.
This brings us to John Connor 4, similar to John Connor 3, he splits off from the previous John Connor due to the events of Terminator 3.
Now here's what's important, John Connor 1 lives in world 1.
We know the humans win world 1. World 1 has no time interference. World 1 sends back the 101 creating world 2, where the original Terminator takes place.
John Connor 2 lives in world 2, we know the humans win world 2, because they sent back the T1000 after losing again, which creates world 3, where T2 takes place.
John Connor 3 lives in world 3, we can assume that John Connor wins this war as well, because he's still the primary target, and they decided to send her back and roll the dice. If they lost the war, they wouldn't have sent her, because killing him and his officers creates a different world where they might lose. Sending her back creates world 4, where Terminator 3 takes place.
She does however successfully kill a lot of his officers, and they do put him in the bunker where he probably wouldn't have been before which changes things around some. They also potentially spooked him, or altered him due to any number of important things that happened to him, like changing how he meets Kate Brewster, telling him of his own death. This things lead to a World 4 that's not going to play out exactly as World 3.
Now it's highly likely that World 3 and 4 are drastically different than World 1 and 2, because Terminator 2 delayed the war for many years, leading to an older John Connor at the start of the war, and different, potentially better technology for the machines at their start. Also changes a lot of other things. Humans born that wouldn't have been. Humans older than they would have been. Humans dead who wouldn't have been. Humans in different locations when the war started. Different humans killed by the nukes.
Now if this isn't complicated enough, we can try to make sense of the Terminator, Sarah Connor chronicles. This follows a John Connor 3, as he's split off by the events by the TV series from the other John Connors. Can this be canon and world 3/4 be canon as well? Well no. World 3, created by Terminator 2, follows 1 path - either the TV show or terminator 3. If the Terminators in World 3 send back the Terminatrix and create World 4, then World 4 is created and World "TV Show" isn't. Both concepts however split off based on World 3 turning into their own world 4s.
Back towards the main movie canon. Here's a problem...
In world 3, following the events of T2, before the Terminators send back the T1000, they must send back the 101, to create their own world. If they don't, then they don't exist to send back the T1000. In world 4, following the events of T2, they must send back the original 2 terminators, despite being in a drastically different future, in order to create World 3 again.
In order for this to be possible, we must assume that despite coming from different futures, the 101, 1000 and Kyle create the same results when sent back to continue the chain. The T1000 for example, who was sent back by world 3 before they sent back the Terminatrix, can't be stronger or smarter and kill John Connor, or else World 3 doesn't exist. The paradox being, that the exact same time warriors must be sent back, every cycle, despite coming from different worlds, or else the differences must be so slight that they don't cycle through the loop and still affect anything by the time their next versions are sent back.
This could only happen due to a major coincidence. It would mean that the machines built an near identical 101 and 1000 despite the war happening 10 years later, and Kyle was nearly an identical soldier despite the war happening 10 years later, as well as the leader being affected by the events of the movies.
It's not... technically... impossible. It's possible that despite coming from a different world, they are similar enough that he goes back and time and does the exact same thing. It has to be pretty exact though, if he and Sarah Connor make love in a different way, or a different time, she might not be impregnated, or perhaps a different sperm of his mixes and created a different John Connor 3 or 4. This is possible though, if John Connor can win the war with a different father, or a different upbringing, he can continue the cycle being born from a different sperm.
Also possible that minor details did get transmitted but didn't break the cycle. Maybe Kyle sent back from World 3, having not been quite as hardened by the delay of the war's start, was a little bit slower, and Sarah Connor lost a finger while he was protecting her. This may affect John Connor, and in turn affect the war, but the cycle continues. For all we know, in Terminator 3 - that dead Sarah Connor had a missing finger that we never saw, because their past was slightly different than the events of Terminator 1 and 2.
Now it doesn't matter if time is splintered or singular, only matters that the events stack. Meaning, John Connor from Terminator 3 remembers the events from Terminator 2, and Sarah Connor from Terminator 2 remembers the events from Terminator 1. For this to be possible, the above analysis must be true.
Yes I realize it's just a movie. I just like that kind of analysis.