Drawing out the spacetime diagram does make it very easy to understand
an observer places a stake a point along the path of a moving platform/ruler what have you (an object with length), the stake is marked point A, he plans to determine the length of the moving platform as it passes by he will mark when the front end passes A and when the back end passes A, thus with his eye he will have "measured the length" not numerically but have an understanding of about how long the object is.
As the front of the platform moves past point A the light of this event travels towards the observer so he may say that the front has passed. For very fast objects near the speed of light, the back end will pass point A possibly even before the front event has reached the observers eye, and so the back event light would be propagating very quickly toward the observer who had just noted the front had passed and now has found that the back came across point A very quickly so that the length of the platform must be very short.
Does this sound correct?