That is absurd. Basic thought experiments make it plainly obvious why time slows for a moving body.It doesn't seem like your question was satisfactorily answered. Which is ok because, afaik, it's an open question in physics in the sense that there's no physical, mechanistic explanation for relativistic differential aging.
If you start with two identical clocks side by side and accelerate one clock to, say, .5 c and then decelerate it and bring it back alongside the stationary clock, then the moving clock will have recorded less time than the stationary clock.
If the clock engines are, say, vibrating quartz crystals, then that means that the period of oscillation of the crystal in the moving clock was, during the round trip, on average greater than that of the stationary clock.
How does this happen? What's the mechanics of it? Nobody knows. It's one of the outstanding mysteries of physics.