how glucagon and insulin antagonistic in nature?

Insulin and glucagon are hormones, they control/balance the blood sugar level in the body. They both are produced in the Pancreas (Langerhans Islets), Insulin by the beta cells, and Glucagon by the alpha cells.

They are antagonistic, meaning, they have opposite effects:

• If the blood sugar (glucose) level is high, insulin is released. Insulin lowers the level by certain reactions (skeletal muscle cells and fat cells remove (and store) more glucose, also more glucose gets converted to glycogen in the liver, - also fot storage -, etc)
• If the blood sugar (glucose) level gets low, glucagon is released. Glucagon activates the stored glycogen to convert back into glucose and be released into the blood stream, thus raising the level.

In healthy individuals these 2 hormones keep the blood sugar level in balance.