Why seismic S wave doesn’t pass through the liquid medium
A seismic S wave is a shear wave, which moves particles perpendicular to their direction of propagation. They can propagate through solid rocks because these rocks have enough shear strength.
Why seismic S wave lack shear strength?
The shear strength is one of the forces that hold the rock together, preventing it from falling into pieces. Liquids lack shear strength.
This is the reason why if you take a glass of water and suddenly remove the glass, the water will not keep its shape.
In fact, it is just a matter of rigidity: S waves need a medium that is rigid enough for them to propagate. This is why the seismic S wave doesn’t pass through the liquid medium.