Relativity is a rather easy concept to understand.
2 objects in relative motion can each consider themself at rest independently. In doing so, the rest object sees the other's clock dilated and spatial length contracted. This observation is reciprical when each observer considers themself at rest.
When a Muon and Earth are two objects in relative motion, distance is only contracted for the Muon because the atmosphere in which it is "moving through" is "moving with the Earth". There is no reciprical effect in this case because that wouldn't make sense.
And finally, when an object approaches c, the spatial contraction between two distance objects as measured from the frame that sees said object traveling near c, goes to 0 for the moving object. The object approaching c does not experience the same type of length contraction as the Muon above, because that just wouldn't make any sense - how could the distance possibly be close to 0?
Let me add the twin paradox for good measure. Two objects in relative motion meet at some point in time. In order for them to meet, one of the objects had to undergo an acceleration for the return trip to begin. The object that accelerated experiences the "real" time dilation/length contraction effect because, well, he accelerated.
See, easy to understand, where is the problem?