Looper - The remaining question answered

I just watched Looper a couple of days ago. It was a slight disappointment, but still pretty close to anticipations: an interesting concept in a relatively entertaining package that just happens to demand a bit too much forgiveness from the viewer in terms of how the time travel logic plays out. It also features elements that go unnecessarily far from its basic premise.

But even if you're willing to accept the weird time travel rules depicted in the movie, there is one crucial question that remains to be answered. Here's an explanation, which is kind of related to a funny theory that has been circling the discussions related to the movie. If you don't want to be spoiled, don't read forward, but otherwise click below.

Show/hide the question and the answer

In the movie Cid has somehow become the evil rain maker due to having his mother killed. But in the movie we only see old Joe about to kill the mother due to knowing that Cid is about to become the rain maker. So how did Cid become the rain maker in the first place?

Here's how. The story starts with Seth, who is the real reason behind Cid becoming the rain maker.

1. Seth is born in 2070, but Seth's parents have powerful enemies that want to avenge Seth's parents by sending him back in time to be killed by loopers.
2. In early 2074 Seth's parents decide to save Seth by sending him back in time by themselves to a safer location.
3. 4-year old Seth gets adopted in 2020.
4. Young Seth has hardships in life and is recruited as a looper.
5. While young Seth is working as a looper, young Joe A gets to kill old Joe zero.
6. Young Seth becomes old Seth A.
7. Old Seth A gets sent back in time.
8. Young Seth B fails to kill Old Seth A, because Old Seth is singing a song he learned in 2073 when he was there for the first time at the age of 3.
9. Seth's parents in 2074, having sent their kid back in time, experience the changed past and read how a man they recognize as Seth got brutally killed by loopers. Seth's parents decide to resort to their secretly developed fail-safe bottle-sized time machine and send a note to themselves 6 months back.
10. Seth's parents get the message in early 2074. They decide to send Seth to 2043 instead of 2020 and even fake a birth certificate to fool the bad guys.
11. 4-year old Seth gets adopted in 2043.
12. The crime bosses are somehow able to find out the specifics of Seth's birth certificate so that they know the assumed birthdate and the hospital area code. They then order the boy to be killed.
13. By mistake the gangsters in 2044 do not go for the small Seth, but the small Cid instead. The mother tries to defend the kid and gets killed in the process. Cid manages to escape through the use of his TK abilities, but becomes filled with hatred.
14. Cid grows to be the rainmaker.
15. In 2070's Cid takes over and starts closing the loops.
16. Old Joe A gets sent to 2044 and manages to escape young Joe B.
17. Having received the numbers of the birthdate and hospital old Joe A goes to kill young Seth when trying to prevent the existence of the rain maker. 
18. Seth gets killed for the third time: first as an old guy who's mutilation took place through time, then as a younger just mutilated guy, and chronologically last as a kid. Poor Seth.

So there you have it. It's all very obvious! Cid is not Joe. But Seth is the killed kid. :)