Question

Why does it make metabolic sense for the same hormone signal to stimulate glycogenolysis and inhibit glycolysis in the liver while stimulating both glycogenolysis and glycolysis in muscles?

Answer 1

This is because if the two  metabolic processes were to be  active at at the same time;  

Two molecules of ATPs and Guanosine triphophate (sometimes used for  energy transport) will be expended per each cycle, with no  compensatory rate  of replacements present  at the moment in the cell,this  affects cell metabolism for energy availability

2 Both Glycolysis and Gluconeogensis are both exergonic processes  in cells.  The  heat energy liberated from these Calorinogenic effects  will be higher than what the natural thermodynamic barrier of cells can withstand. Consequently;  the heat will raise temperature of the cells affecting metabolic activities of hormones and enzymes which are (proteins) ,and easily denature by high temperatures.    

However, in muscles cells,gluconeogeneis is a compensasory process of Glycolysis. This because during active exercise with high metabolic demand in muscles cells, glucose is rapidly metabolise  to to pyruvate,(but not at the rate that the Citric acid  cycle can  metabolise) for Lactic acid production by muscles cells for energy production.  Pyruvate must be broken down rapidly so that NAD+ will be available for  Glycolysis to continue. Therefore  to sustain Glycolysis at this rate  continuous supply of glucose is supplied  from Gluconeogenesis.