The asymmetry in the perception of time dilation arises from the relative motion between observers and the principle of relativity. This principle states that the laws of physics should be the same for all observers, regardless of their relative motion, as long as they are in an inertial reference frame (i.e., not accelerating).
In the scenario you described, where you are at rest and your friend is moving, the key factor is that your friend is the one undergoing acceleration and deceleration to change their velocity, while you remain in an inertial frame throughout. Acceleration introduces a preferred reference frame, breaking the symmetry between observers.
When your friend accelerates and changes their velocity, they can be considered to have changed reference frames. In their new frame of reference, they are at rest, and you are the one moving. According to the principle of relativity, they will perceive time dilation and length contraction relative to you. This means that from their perspective, you will appear to age faster, and your length will be contracted in the direction of your motion.
On the other hand, from your perspective, your friend undergoes acceleration and deceleration, which breaks their inertial motion. As a result, they are not in a single inertial frame of reference throughout the entire journey. The asymmetry arises because they experience the effects of acceleration, while you remain in an inertial frame without undergoing acceleration.
In summary, the perception of time dilation depends on the relative motion and acceleration between observers. The principle of relativity ensures that each observer perceives the other as experiencing time dilation and length contraction, but the asymmetry arises because one observer is undergoing acceleration and changing reference frames, while the other remains in an inertial frame.