What is the purpose of gluconeogenesis?
Gluconeogenesis is not the reversal of the glycolysis, but the generation of glucose from non-carbohydrate precursors (like odd chain fatty acids and proteins). The reason why we have this process is because some organs and tissues can only use glucose as their energy source. These include the brain (although ketone bodies can be used here as well), erythrocytes, testes and the kidney medulla.

Usually the glucose for the supply of these tissues comes directly from carbohydrates in food or storage carbohydrates as glycogen or starch, but when these are not available, the body has another way to get around this problem and to avoid the starvation of these tissues. See for example here and here.