Question on Length contraction (relativity)?

If the beams arrived back at S at the same time from the stationary observer's point of view, that would mean that there is a universal time for measuring all events. But Einstein said exactly the opposite, that there is no universal time. He said that because he knew that from the stationary observer's point of view, the beams would not arrive back at S at the same time even though the moving observer would see a simultaneous arrival. The stationary observer sees moving observer contract in the direction of motion, but the moving observer remains in his central position.