Time dilation is mutual, according to special relativity. Yet the retardation of a clock can only be demonstrated (calculated) if that clock is allowed to travel, that is, allowed to move from point A to point B, in some inertial system. If the scenario craftily precludes such a travel for one of two clocks in relative motion, time dilation becomes effectively asymmetrical - only the other clock's retardation can be demonstrated.
This is the whole secret behind the so-called twin paradox. The travelling twin/clock is allowed to move from point A to point B in the sedentary twin/clock's system, but the reverse is impossible for the simple reason that the travelling twin/clock's system is, in the scenario taught by Einsteinians, point-like (consists of a twin and/or a clock and nothing else).
As soon as the relativistic scenario is changed and the sedentary twin/clock is seen moving from point A to point B is the travelling twin/clock's system, Einstein's relativity dismally falls apart:
A clock on the ground is stationary and a train moves towards it. When the clock at the front end of the train passes the stationary clock, an observer on the ground sets the stationary clock to read the same as the front end clock. Finally, while the train and the stationary clock are still in contact, the train stops and the train's clocks simultaneously (as judged from the train's system) stop ticking. That is, at 5 o'clock (train time) all clocks on the train stop both moving and ticking.
Two important observations:
1. Immediately after the stopping of the train, clocks on the train read 5 o'clock while the clock on the ground reads less - say, 4 o'clock (according to special relativity of course). That is, the clock on the ground has been running slow.
2. As the clock at the front end of the train stops, it has just finished the outward leg of the journey described in the usual relativistic scenario. However, since the new scenario has allowed the clock on the ground to move from point A to point B in the train system, the conclusion is different: the travelling clock (at the front end of the train) shows more time elapsed than the stationary clock on the ground (the travelling twin has grown older than his sedentary brother).
Already at this stage the absurdity is obvious so there is no need to finish the story by considering the inward leg of the journey.