Yes, so? It has nothing to do with the subject being discussed, nor with the fact that two people have explained to you that you are wrong and why you are wrong, yet you persist.
This is not what you said initially, you claimed that "Everyone will agree on what time the two passing clocks read at the moment they pass each other." When I showed you that the claim is false, you changed your tune. Besides, now you are talking about "order of events" and this exercise is about elapsed proper time. I cannot teach you, I am sorry.
Then we are done. He denied it, that was my point.
Incorrect, there is an infinity of observers that will actually disagree that B and C show the same time. Only one observer agrees, that observer is the one that measures B and C to move with equal and opposite velocities wrt him.
No, he needs to transfer the reading on clock B to clock C. He even admits to that in the OP (it is a well known scenario, he copied it from somewhere without fully understanding it), nevertheless he later denies that such a transfer of information from the frame of B to the frame of C is necessary.
Well, this is a common fallacy believed by generations of naive students. There is acceleration in the scenario that you depicted (it is a well known scenario). Except: IT IS HIDDEN! When B and C pass each other you need to transfer the information (clock reading) from B to C, i.e. you need to JUMP from the frame comoving with B to the frame comoving with C. As Markus pointed out, acceleration is key in creating the necessary conditions for the paradox to exist.
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