Sugar polymerize to form several polymers like glycogen, cellulose, starch, chitin. Glycogen is a sugar polymer which acts as a reserve energy source in muscles in animals.
Cellulose is a sugar polymer that makes the cell wall of plant cell and starch is a sugar polymer that acts as energy storage form in plant cells. Protein can not be formed by sugar polymerization in long-chain because sugar is not the monomeric unit of protein and the monomeric unit of protein is amino-acid.
Therefore amino acid is required to be polymerized to form proteins.