Shock absorbers are acted upon by a compressive force ad under compression the objects tend to fail due to brittle fracture, i.e., they break like glass or as brittle material breaks under compression. Now, though steel has more elasticity but it is more brittle than the rubber and when the shock absorber goes under high compression the shock absorber made of steel will have more tendency to break.
While rubber being one of the least brittle material that is known and has comparatively good elasticity (the two factors needed to be kept in mind while selecting a good material for shock absorber) than others available is one of the best choices available to make a shock absorber.