Symmetries is not time going backwards. A electron mathematically transformed into a positron does not state that time suddenly backed up there. To me this situation is the same as some people imagining that because we find a time symmetry, enabling us to play a movie of a ball bouncing backwards, we can also assume that the arrow can change direction. That's not true to me, it's just logic and causality making sense of our lives, presenting us with a ordered past, a 'present', and a future. If that ball movie would give you something else than the bounce, if played forward, then we would meet magic.