We know that glucose molecules are subtracted and added from the non-reducing...

Because they are required as substrates for the enzymes of glycogen metabolism. Glycogen is cleaved from the nonreducing ends of the chain by the enzyme glycogen phosphorylase to produce monomers of glucose-1-phosphate. Similarly, new glucosyl residues are added to the nonreducing ends of glycogen by the enzyme glycogen synthase which can add glucose residues to polysaccharide chain of four or more residues. Thus glycogen synthesis requires a primer. The primer is a protein called glycogenin which contains a oligosaccharide of alpha-1,4-glucose residues attached to a phenolic oxygen of a tyrosine residue.