There are two reasons. But first a little terminology. Blood cells with nuclei are nucleated. Blood cells without nuclei are enucleated. One, mammals are younger in natural history than birds. Before mammals, nucleated blood cells were the norm. read more
The reason may be that nucleated red blood cells allowed birds, and many other animals before mammals, to regulate bloods; however, it just didn’t work for mammals, which is why mammals evolved enucleated red blood cells. read more
The reason that human (acutally all mammalian)mature red blood cells lack a nucleus appears to be so that the red blood cell has room for more hemoglobin and therefore can carry more oxygen per cell. Remember the human red blood cells doen't always lack a nucleus. Up until the final steps of red blood cell maturation, they do have one. read more