As I understand, one of the Special Relativity roots is the statement that two events SIMULTANEOUS in one inertial frame are NOT necessarily simultaneous in another inertial frame that is moving against the first one. To illustrate and PROVE this statement Einstein gave his well known example with two lightning strikes and the observers on a station and in the passing by train. But the FACT (proven by the Michelson-Morley experiments) is that BOTH observers DO see the strikes simultaneously, and it is only a deduction from his "way of thinking" that the station observer concludes that the train observer sees the front lightning before the rear one (and vice versa for the train observer about the station one). STRUGGLING TO UNDERSTAND this example I do NOT see that it illustrates the absence of simultaneity. On the contrary it seems to raise the question about possible simultaneity of events for all inertial frames, moving against one another. I hope you understand my plea for help and will show me how to get out of my conundrum. Many thanks for attention.