Why would glucocorticoids promote glycogenesis and not glycogenolysis?
Glucocorticoids have a number of physiologic effects on glucose metabolism, inflammation/stress response, bone metabolism, etc. In general they are called glucocorticoids because they were originally found to be associated with increased blood glucose concentrations. Simply put, glucocorticoids antagonize the actions of insulin and create a state of insulin resistance, as well as increasing the expression of enzymes involved in glucose metabolism. They have a number of effects on all sorts of tissues and biological processes.

With regard to your question specifically, it makes sense that glucocorticoids stimulate glycogen synthesis, because it will allow the body to store more glucose as glycogen and increase the body's capacity for liver glucose production (i.e. glycogenolysis). Remember, at the same time glycogen synthesis is being increased, the glucocorticoids are inducing a peripheral insulin resistance that antagonizes insulin action in skeletal muscle and fat that also leads to increasing glucose concentrations in the blood. Moreover, free fatty acid are released from adipose tissue to be carried via the circulation to the liver so they can be oxidized to produce ATP for gluconeogenesis. 

There is an excellent chapter that describes the effects of glucocorticoids on glucose metabolism in the major metabolically-active tissues (e.g. liver, white adipose tissue, skeletal muscle) by Kuo et al from Vol 872 of Advances in Experimental Medicine and Biology (pages 99-126). The book is not open access so I can't paste a picture of any of the figures, but they essentially show what I describe above. Here is another link to a very nice review article in the Journal of Endocrinology that has some great figures showing fuel redistribution in response to glucocorticoids as well.