If sound is a longitudinal wave, then why it is demonstrated with the help of a transverse wave not with the help of a longitudinal wave itself?

Good observation. While sound itself is a longitudinal wave, the transverse graph is actually the movement of a particular column of air. 

You must have read that in a wave, the medium does not move but the energy gets transferred. The particles move to and fro with respect to their positions. The transverse graph represents that to and fro movement of the particles.

I hope this helps you. Cheers!