What is the reason for isotropy in amorphous solids?
Assume that the spheres in the drawing are atoms.

In the second picture atoms are not orderly arranged. No matter where you go in crystal of a amorphous solid, the disarrangement will be same. Since in every direction, disarrangement is same, physical properties along every direction is also same. Therefore, amorphous solids are isotropic.

In the first picture, the arrangement is orderly. So, when you go in any direction, the arrangement will be different. It is also clear in the rectangles shown in the picture. Try doing it yourself on a piece of paper. Try finding any four different directions along which the arrangement is same. 

Ps: Ignore my poor drawing skills.