S-waves are shear waves, which move particles perpendicular to their direction of propagation. They can propagate through solid rocks because these rocks have enough shear strength. 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. S-waves need a medium that is rigid enough for them to propagate. This is why S-waves cannot propagate through liquids.

P-waves travel through liquids and gases as well as through solids. Although liquids and gases have zero rigidity, they have compressibility, which enables them to transmit P-waves. P-waves are predominantly compressional waves. As a P-wave passes, material compresses in the same direction the wave is moving. Sound waves are P-waves moving through the air.

P waves travel fastest and are the first to arrive from the earthquake.  In rock, S waves generally travel about 60% the speed of P waves, and the S wave always arrives after the P wave.

Source: NCERT