The time dilation is not the result of observation of a physical phenomenon. This is a mathematical relationship disguised as physics.

As Einstein in " on electrodynamic of moving bodies 1905 " t is the time a light beam needs to reach the moving mirror, and that is t=x'/(c-v) and t'=[x'/2(c-v) + x'/2(c+v)] and the difference, t-t'= vx'/(c-v)(c+v). the rest are derived from the definition of time. The whole story is about a definition. And the result is: if we calculate the time acc. the definition, it would lead to a difference in the calculated time of an event calculated by an observer in two systems with relative velocity v.

In any case, if you are against my opinion that time dilation is only the observer's perception of time in the opposite system, you defend the contradiction that the clocks in the first system are slower than the second system, and in the second system slower than the first system!

the root of the problem can be found in "On the electrodynamic of moving bodies " , where Einstein derives the equation relating t and t'. Please read again the 10 pages at the beginning of the paper

if really the clocks run slower, it should apply to both frames without discrimination and logically it is impossible. Censorship does not belong to the lovers of science.

it is obviously unlogical that at the same time, both of the 2 clocks run faster than the other one. It is only possible if it is an observer-dependent appearance of reality. for example if a body approaches the observer with v=0.5c , the observer would see 2 events with "Δt'=2" , in only "Δt =1" hour