In the twin paradox, one twin remains on Earth while the other twin travels away in a spaceship and then returns. If the traveling twin only travels in the opposite direction, there would not be a continuous and indefinite appearance of time dilation for both observers.
The twin paradox arises because the traveling twin experiences acceleration and deceleration when changing direction, while the stationary twin on Earth remains in a relatively constant frame of reference. The acceleration and deceleration experienced by the traveling twin are what break the symmetry and lead to the difference in their aging.
When the traveling twin accelerates and changes direction to return to Earth, they experience a change in their inertial frame of reference. During the period of acceleration and deceleration, the traveling twin's frame of reference becomes significantly different from that of the stationary twin on Earth.
As a result, the traveling twin will experience time dilation during the periods of acceleration and deceleration, but their time will appear to "catch up" with the stationary twin during the periods of constant velocity in between.
From the perspective of the stationary twin on Earth, they would observe the traveling twin's time to be dilated during the periods of acceleration and deceleration, but when the traveling twin is moving at a constant velocity, their time would appear to progress at a similar rate as the stationary twin's time.
Therefore, in the twin paradox, the time dilation effects are not indefinite but occur during specific phases of the journey when the traveling twin is undergoing acceleration or deceleration. The asymmetry of the motion and changes in the frame of reference are crucial in causing the time dilation discrepancy between the twins.