Why is mammalian RBC not nucleated?

Red blood cells lose their nucleus completely as they mature. This is an adaptation in order to carry more oxygen around the body.
Each cell is packed with a protein called haemoglobin, which attracts oxygen very strongly. The oxygen passes from the air in the alveoli and into the blood through the alveoli and capillary wall. Because the red blood cell has no nucleus (which would be a large spherical structure in the middle of the cell) it can use all of its volume for haemoglobin, so can carry as much oxygen as possible.

Its other adaptation to its function is that it has a biconcave shape - this enables it to have a large surface area for picking up oxygen in the first place.