If light-speed is invariant,why RoS exist?

[ash64449]

This is a question from Einstein's thought experiment.

This thought experiment is found in this article: http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

For those who know that thought experiment,i would like to ask a few questions.

To an observer outside two lightning striking the train are simultaneous.

Well,we know that light speed is invariant,it travels at the same speed regardless of whether the observer is moving or not.

Well,there is an observer in train.
Train is moving in uniform motion. Since rest and uniform motion are indistinguishable in his reference frame,he considers himself as at rest. lightning strikes are simultaneous in outside frame,we know that light travels at the same speed. So light from both the lightning strikes must reach the observer in train in the middle at the same time,because light speed is invariant regardless of the motion of the train. So Observer in the middle of the train must come to the conclusion that lightning strikes are simultaneous.

Yet Einstein's thought experiment says that this cannot happen. Why?

 

[pervect]

Draw a space-time diagram, from the stations point of view. The two light signals will meet at the midpoint in the station frame. The train will have moved since then, however, so that won't be the midpoint of the train.

 

[Henriamaa]

The observer in the train is moving toward the lightning strike ahead and moving away from the lightning strike behind. This observer is not in the middle.