Let's say we have two observers, one stationary and the other moving at relativistic speeds. The observers agree to emit a flash of light when their clock reads 10 seconds. I think it should be possible to arrange it so that the stationary observer is in the same location as the moving observer when the stationary observer's clock reads 10 seconds (although I don't think that this should matter). It seems like each observer should release their light before they observe the light from the other person, but this doesn't really seem possible physically. If one of the observers sees the other person's light before they emit their own, then it breaks the symmetry of relativity.
Can anyone give me some physical intuition for this?