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The Islets of Langerhans in the pancreas contain different types of cells that secrete specific hormones. The two primary cell types are alpha ($\alpha$) cells and beta ($\beta$) cells.
The $\beta$-cells are responsible for the secretion of insulin, which lowers blood glucose levels. Thus, statement (A) is correct.
The $\alpha$-cells are responsible for the secretion of glucagon, which raises blood glucose levels. Thus, statement (B) is correct, and statement (C) is incorrect because $\alpha$-cells do not secrete insulin.
Glucagon acts on the liver to stimulate glycogenolysis (the breakdown of glycogen into glucose). Thus, statement (D) is correct.
Final Answer: (C)