Usually length contraction is presented as a contraction of the moving spaceship (in its direction of motion) as measured by someone at rest. The challenge then is to understand why the moving spaceship, "being short" measures the at-rest ship to be short and not long, as in this animated GIF:
The "top-down" approach quotes Einstein's principle of relativity: Every inertial reference frame should experience the same physics, so in this case everyone moving relative to a reference frame should be measured as contracted relative to the frame.
This seems contradictory when you first learn Special Relativity, but remember that SR is about would you measure, not what is in some absolute sense.
In the "bottom-up" approach, championed by John Bell (of Bell's theorem) and developed before Einstein by Lorentz, Larmor and Poincaré, you consider moving clocks to contract, slow down and not being synchronizable. So the moving spaceship would then have "messed-up" measurement equipment, and use it to measure the at-rest ship to be shorter than than the moving one. John Bell favor this as more intuitive, and wrote an essay, "How Special Relativity Should Be Taught."
Bell's bottom-up approach is animated in the following video at youtube: