That the only symmetric part about this thought experiment, is the symmetry in motion... not the way the experiment is set up. Simultaneity is not absolute, therefore the relative observers need not agree on a definite moment for "tick" to occur on respective clocks.
So John can say H-clock of Bob is in motion, while Bob can validly proclaim that it is himself that is at rest while John's H-clock is in motion.
You have two choices: (A) the clocks started motion at same place at same moment in time (synchronized), or (B) the clocks started motion from different locations in space at different moments in eachother's respective time (simultaneity is relative, therefore by being at different locations in space, neither can agree on whether clocks were actually synchronized. One says yes while the other says no! Past and future are relative to the observer; there is no universal "past" or "future". Signal of light must have enough time to "link" respective events in relative frame (causality), thereby distinguishing past from future (which only counts for one, not necessarily both, of the observers. In other words my past can be your future)).
Because of the symmetry of inertial reference frame, both are equally permitted to contest that it is himself that is at rest while the other is in motion. This permits John to say that H-clock of Bob "ticks" slower; likewise Bob can say that John's clock ticks slower. Both can record their results and bring the clocks and notebooks before a judge & jury to analyze. Paradoxically, they both win the case. Nothing went wrong here... this is an intrinsic aspect of relative motion. Both have equal stake in valid claim that the other is aging slower!
The twin paradox implies that as John and Bob pass eachother on by, they simultaneously synchronize their clocks. Upon joining the two once again after a lengthy trip, you immediately realize that even though both can validly contend that the other was aging more slowly, they can't both be older than eachother. The resolution lies in the fact that one of them had to make the decision to turn around and come back, thereby shattering any preservation of symmetry. By turning around (changing direction and/or speed of velocity vector), an acceleration will take place which more than compensates for any discrepancy in who can validly claim to be the "older twin". Motion is no longer symmetrical after acceleration has taken place; this asymmetry is the determining factor in nature's choosing between who is actualy older & who is younger.