Firing counter-propagating photons inside a moving train

Question

This is sort of a follow-up to my other question, in which you have the following scenario:

Have a photon gun firing two counter-propogating photons from the center of a moving train. The observer inside the train sees both photons hit the ends of the train simultaneously, whereas an outside observer sees the photon hit the rear-end of the train first.

However, why would the the observer inside the train see the photons hit both ends simultaneously? Since the speed of light is unaffected by the velocity of the train, and since the back end of the train is moving towards one light pulse while the front end of the train is moving away from the other, shouldn't it be logical that the person inside the train will also see one photon hit before the other?

Answer 1

since the back end of the train is moving towards one light pulse while the front end of the train is moving away from the other

This is not true in the reference frame of an observer on the train. In that reference frame, neither end of the train is moving.

It is true in an external observer's reference frame, and that is why an external observer sees the rear-pointed photon hit first.