This is an incomplete description of insulin and diabetes. This article only address Type 1 diabetes where the insulin is lacking due to pancreatic insufficiency.
In type 2 diabetes, the opposite happens. There is too much insulin in response to high blood glucose, the cells response by increasing resistance to the insulin or become de-sensitized to the insulin. The pancreas then responded by increasing insulin production even more and the cells responded by increasing insulin resistance even more. It becomes a tug o war game between the pancreas and the cells.

Because insulin cannot push glucose into cells due to insulin resistance nature of the cells. The insulin has no choice but store glucose in the blood as glycogen in the liver and adipose tissue. It creates the paradoxical effect where, the cells are starving for glucose and cannot produce energy but the liver is turning fatty from glycogen over-store and adipose tissue is expanding.