So we know that insulin allows for GLUT-4 transporters to be added within muscle and adipose tissue. The purpose of Glucagon is to stimulate catabolism (such as gluconeogenesis, glycogenolysis, etc) to increase circulating blood glucose, but what good is circulating blood glucose if it cannot be moved into the cells for utilization (glycolysis to generate ATP)? So glucagon upregulates a proportionate insulin release allowing for GLUT-4 transporters to be placed within tissue for glucose uptake. The amount of insulin release is not enough to actually oppose the catabolic effects of glucagon however.
Insulin doesn't have this effect with glucagon. So during a fed state, the insulin spike is inversely correlated with the amount of circulating glucagon.