The reason we need to synchronize clocks is that in physics, we need clocks that keep accurate and precise time. We might want to make measurements of time intervals in two reference frames in relative motion with each other, and we generally want coordinate transformation equations to be consistent with the two postulates of relativity.
So, how do we synchronize clocks? We can use a flash of light at the midpoint between 2 clocks, with photocells to detect light and in the same IRF. This would synchronize the 2 clocks.
However, let’s assume that 2 observers are in different IRFs. One is with the 2 clocks to be synchronized, the other is far away, and their relative velocity is nonzero. The observer from one IRF would see that the clocks in the second IRF are not synchronized, but the other observer would see that they are.
Who’s right? Both are objective and correct because of asymmetric relationship of space and time between 2 frames of reference.