Errors in Einstein's Reasoning (4)

In Part I, Section 09, "The Relativity of Simultaneity", Einstein explained the concept of simultaneity this way:

If two beams of light are sent out simultaneously from two points on the railway embankment, then they will reach an observer in the middle of the embankment at the same time, but will reach an observer in the middle of a moving train at different times. Thus the two observers will not agree on the simultaneity of the two beams of light.

Here Einstein messed up the concept of simultaneity. In his example, there are actually two types of simultaneity: one type is for the sending of the light, another type is for the perceiving of the light. The two observers cannot agree on the simultaneity of the arriving of the two beams of light, but can agree on the simultaneity of the sending of the lights, if they take the motion of the train and the speed of light into account.

Instantaneity is an important concept of time, but it is often being ignored. When we talk to each other in close range, or when we are looking at something, we never think about how much time it takes for sound or light to reach us. Basically we assume a kind of instantaneity unconsciously, where the happening of an event can be immediately perceived by us. But we know when to consider that delay, like in trying to explain the echo from a wall, or the principle of Radar positioning.

This on and off nature of instantaneity might have played a role in Einstein's perception of simultaneity.