Could look at the chicken and egg argument for closed loops, i guess. To get the egg, it has to be layed by a chicken, which has to hatch from an egg, and so forth. That functions as your closed loop. Still need the proto-chicken to lay the first chicken egg and get you started, though. I'm thinking of this timeline the same way: First time through, you got to 2018 with something similar, but not quite the timeline we're familiar with. They went back and spawned the current timeline, which is now self-sustaining and a nice little closed loop.
I see what the problem is here. You are, in your mind, and probably unintentionally, creating a second time dimension, so that you can represent non-linear time-travel as a linear function, which is easier for people to wrap their heads around.
However, there is no second time dimension. Time defines the order of events. Kyle Reese appeared in 1984 first. Period. There are no future events before that. Though Kyle remembers these things, they haven't happened yet, from the point of view of an outside observer. The event that causes Kyle to be sent back happens after, from the point of view of the outside observer. This isn't illogical, because time only has one dimension. There is no such thing as a previous future or an original future.