The classic example of time dilation is "an astronaut flies around the earth at near the speed of light a few times and returns. Everyone has aged more than him." I assume that holds true but I always wondered, if speed is relative why is the astronaut the one moving fast and not the earth or both.

Are you saying that because the act of orbiting or going in a circle around the earth involves acceleration perpendicular to the direction of travel, that the speeds are not relative and the astronaut can be determined as the one that is in fact moving fast?