Without Sebastian, Ciel would not have survived his brief (and not complete) recovery period. Let’s say, hypothetically, Ciel made it out from the cult. He didn’t get a demon, but he still took his brother’s name. Why do I think this?
This is something he asks of Sebastian whenever something jarring happens, something that triggers his PTSD. This was just the first incident, and it is obvious Ciel was very shaken. As Sebastian said, Ciel often “screamed himself awake”. The contract states that Sebastian must keep Ciel from harm, and that includes harm he may cause himself physically. I cannot speak into how it is to survive the trauma he survived, but I can image it is a traumatizing recovery in itself. He had no coping devices, and being who he is (self-loathing and feeling he deserves doom - maybe due to survivors guilt or other factors) I wouldn’t be surprised if he turned to self destructive behaviors. Sebastian truly saved him from doom (after the literal doom), and I believe he even admits this in Circus. Thus, he has a relationship to Sebastian built on trauma. These types of bonds are very strong, but can also be abusive within themselves. This is also why I don’t think Ciel acts in Murder when he sees Sebastian’s corpse - or at least he went in with the intention to act and was actually triggered when he saw (not only the way Sebastian mimicked his father) that Sebastian was not responding to his orders, hence the “you were not supposed to die!” Also, his reaction here, when he doesn’t know if Sebastian survived:
The one thing Ciel can always rely on is Sebastian protecting his life - from the harm other people wished on him, and the harm he wished on himself. He knows his protector will one day be the one who destroys him, but Ciel knows deep down that he literally and figuratively owes Sebastian his life.
I could just be really late to the party on this but here goes.
Now that the 2 Ciel theory has been confirmed, I went back and watched some episodes in the anime. I rewatched episode 45 in Book of Circus, ‘His Butler, Sneering’. It’s SO blatantly obvious now that there are two kids with Vincent! I would have never second guessed it if this hadn’t been confirmed!
Also note how in each frame there are objects conveniently placed to hide the twin, something most people wouldn’t even think about.
Edit: Originally I had the first pic as Real!Ciel and the second as Our!Ciel, as pointed out by @abybweisse, it is the opposite!