Why can't transverse waves propagate in a gas, but they can in a metal?

Transverse waves are those waves where the displacement of the medium is perpendicular to the direction of the propagation of the wave. For example, the ripples on the surface of water when we throw a stone in it causes transverse waves. The wave propagates outwards from the point of impact, while the medium (water) moves up and down (perpendicular to the wave propagation). Similarly, the waves generated on a piece of string or rope are also transverse waves. 

Transverse waves can easily propagate through a solid since solid particles have equilibrium positions and when disturbed, they will tend to come back to that position. Such is not the case with gases, as there is no fixed position of a gas molecule. There is no mechanism to drive the motion perpendicular to the direction of wave propagation and hence transverse waves cannot propagate through gases.

Hope this helps.