Carbon creates inexhaustible variety because:
1) it can form 4 bonds, hence able to form large and complex molecules. It's valence shell has 4 atoms in different orbitals, so it can covalently bond with four other atoms Each carbon acts as an intersection point from which a molecle can branch off. This is why biological molecule sare so diverse.
2) There are actually only 5 main major elements of life, C,H,O,N,S,P - but carbon is the key for diversity.