system
Given the following post, respond as if you're commenting on Reddit:
human
Why is relativity of simultaneity a consequence of special relativity?

Take for example the famous situation with the train and the embankment, when two lightning bolts hit the front and the rear of the train. The person on the midst of the embankment will see both flashes at the same time and think they're simultaneous (since both flashes are equally far removed from him). The person in the train however would see the flash in the direction the train is moving towards first because the train, from the person on the embankment's perspective, is moving towards that flash while moving away from the other.

I don't think I have any trouble with this situation, but I don't see how this isn't derivable from the physics before special relativity came along. It appears to me is that all you need to know about is that the speed of light is finite and the Galilean principle of relativity, both which were known before special relativity came along.
So the question being: why do we need special relativity in order to explain relativity of simultaneity? Thank you.
gpt
As written, your question mischaracterizes the issue with simultaneity.

It's not a question of the two observers PERCEIVING or SEEING things differently; things are actually different in one frame vs. the other.

In the example you give, even after the observers "correct" for the finite speed of light (which gives a delay between when the flash happens and when it reaches their eyes), the events that are simultaneous for the embankment viewer would not be for the person on the train.

This is inconsistent with Galilean relativity.