An equally satisfying answer, with a similar flavor, to the question of why time dilation and length contraction occur is because of the nature of spacetime geometry.
In the theory of relativity, spacetime is not a fixed and absolute framework. Instead, it is a dynamic, flexible structure that can be influenced by the presence of mass and energy. Mass and energy create curves in spacetime, similar to how a heavy object placed on a rubber sheet causes it to deform.
Time dilation and length contraction arise as a consequence of these curved spacetime geometries. When an object moves through curved spacetime, its path is altered, and the flow of time is affected. This alteration causes time to pass differently for the moving object compared to a stationary observer. The greater the curvature of spacetime, the more pronounced the effects of time dilation and length contraction.
Just as driving a car in a straight line on the curved surface of the Earth eventually leads back to the starting point due to the underlying spherical geometry, the dynamic curvature of spacetime leads to phenomena like time dilation and length contraction. They are intrinsic properties of the spacetime fabric influenced by the presence of mass and energy.
So, in a similar flavor, we can say that time dilation and length contraction occur because spacetime itself is a flexible and curved geometry, and the movement of objects through this curved spacetime causes these effects to manifest.