Why neuron cell not divide?

Neurons stop dividing shortly after birth. The reason is that a neuron's function depends on its state and the unique connections that it has formed with other neighboring neurons. All the neurons in your brain and their connections make up the neural network that defines who you are, your experiences, memories, skills etc. If neurons were to multiply, it would introduce arbitrary nodes and connections into that neural network, interfering with the way it has been trained to operate.