Symmetry and Asymmetry

In some examples, the Special Theory of Relativity considers a symmetric time dilation of two inertial reference frames. But in other examples, such as in the GPS position system where the satellite clocks are slowed because of the satellite velocity, it considers an asymmetric time dilation of two inertial reference frames. As in the cause of the Twin Paradox, the time dilation was simply\textellipsis abandoned! Again an auto-contradiction.